IBMaths: AA SLDPTopic Questions1. Number & Algebra1.2 Exponentials & Logs

Exponentials & Logs (DP IB Maths: AA SL)

Topic Questions

3 hours31 questions

Select a question set to download for
1.2 Exponentials & Logs

Medium
Hard
Very Hard
1a
Sme Calculator2 marks

Find the value of each of the following, giving your answer as an integer.

ln space e.

How did you do?

1b
Sme Calculator2 marks

log subscript 2 space end subscript 16.

How did you do?

1c
Sme Calculator2 marks

log space 25 space plus space log space 4.

How did you do?

1d
Sme Calculator2 marks

log subscript 5 space 500 space minus space log subscript 5 space 4.

How did you do?

Did this page help you?

2a
Sme Calculator2 marks

Let x space equals space ln space 15 and y space equals space ln space 3. Write down the following expressions in terms of x and y.

ln space 5.

How did you do?

2b
Sme Calculator2 marks

ln space 45.

How did you do?

2c
Sme Calculator3 marks

ln space 135.

How did you do?

Did this page help you?

3a
Sme Calculator2 marks

Let r equals log space 2 and s space equals space log space 12. Write down the following expressions in terms of r and s.

log space 24.

How did you do?

3b
Sme Calculator3 marks

log space 3

How did you do?

3c
Sme Calculator3 marks

log space 72.

How did you do?

Did this page help you?

4a
Sme Calculator2 marks

Simplify the following:

fraction numerator open parentheses 4 x y to the power of negative 2 end exponent close parentheses open parentheses negative 12 x to the power of negative 4 end exponent y to the power of 12 close parentheses over denominator 6 x squared y end fraction

How did you do?

4b
Sme Calculator2 marks

open parentheses 2 x to the power of negative 1 end exponent y to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent open parentheses 4 x squared y cubed close parentheses to the power of 4.

How did you do?

4c
Sme Calculator2 marks

square root of open parentheses 9 x to the power of 6 y to the power of negative 2 end exponent z to the power of 4 close parentheses end root cubed space open parentheses 3 x y z close parentheses to the power of negative 2 end exponent

How did you do?

Did this page help you?

5
Sme Calculator5 marks

Solve the equation 2 minus x square root of 3 space equals space fraction numerator 7 x over denominator square root of 3 end fraction comma giving your answer in the form fraction numerator square root of a over denominator b end fraction where a and b are integers. State the values of a and b.

How did you do?

Did this page help you?

6a
Sme Calculator2 marks

Given that log subscript a space 8 space equals 3.

Find the value of log subscript a space 64.

How did you do?

6b
Sme Calculator2 marks

Find the value of a.

How did you do?

6c
Sme Calculator3 marks

Find the value of log subscript a squared end subscript space 8.

How did you do?

Did this page help you?

7a
Sme Calculator2 marks

Let l o g subscript b space 3 equals x and log subscript b space 16 space equals space y

Find an expression for log subscript b space 9 in terms of x.

How did you do?

7b
Sme Calculator2 marks

Find an expression for log subscript b space 4 in terms of y.

How did you do?

7c
Sme Calculator3 marks

Find an expression for log subscript b space 48 in terms of x and y.

How did you do?

Did this page help you?

8a
Sme Calculator2 marks

Show that fraction numerator open parentheses 4 minus 2 square root of x close parentheses squared over denominator 8 x end fraction can be written as 2 x to the power of negative 1 end exponent space minus space 2 x to the power of negative 1 half end exponent plus space 1 half.         

How did you do?

8b
Sme Calculator2 marks

Given that 8 square root of 2 space equals space 2 to the power of a comma find the value of a.

How did you do?

8c
Sme Calculator2 marks

Show that fraction numerator x open parentheses 2 x to the power of 4 minus square root of x close parentheses over denominator x squared end fraction can be written as 2 x to the power of a space minus space x to the power of b comma where a and b are rational numbers. State the value of a and b.

How did you do?

Did this page help you?

9
Sme Calculator5 marks

Solve the equation 16 to the power of x space minus space 3 open parentheses 4 to the power of x plus 1 end exponent close parentheses = 28. Write your answer in the form fraction numerator ln space a over denominator ln space b end fraction, where a and b are integers.

How did you do?

Did this page help you?

10
Sme Calculator5 marks

square root of 425 can be written in the form a square root of b.Find the values of a and b. Show all of your working.

How did you do?

Did this page help you?

11
Sme Calculator5 marks

Solve the equation 4 to the power of x space minus space 3 cross times 2 to the power of x plus 1 end exponent space equals space open parentheses negative 2 close parentheses cubed.

How did you do?

Did this page help you?

1a
Sme Calculator2 marks

Let space f open parentheses x close parentheses space equals 5 ln open parentheses x minus 7 close parentheses.

Find the values of x for which space f open parentheses x close parentheses is undefined.

How did you do?

1b
Sme Calculator3 marks

Given that point straight P has coordinates open parentheses p comma space 0 close parentheses, find the value of space p.

How did you do?

Did this page help you?

2a
Sme Calculator2 marks

Given that 2 to the power of m equals 8 and 2 to the power of n equals 16, write down the value of m and of n. 

How did you do?

2b
Sme Calculator4 marks

Hence or otherwise solve 8 to the power of 2 ? plus 1 end exponent space equals space 16 to the power of 2 ? minus 3 end exponent.

How did you do?

Did this page help you?

3a
Sme Calculator3 marks

Write the expression 3 space ln space 2 minus ln space 4 in the form ln space k, where k element of straight integer numbers.

How did you do?

3b
Sme Calculator3 marks

Hence, or otherwise, solve 3 space ln space 2 space minus space ln space 4 space equals space minus ln space x.

How did you do?

Did this page help you?

4
Sme Calculator5 marks

Solve the equation 49 to the power of p plus 4 end exponent equals 35 to the power of 2 p end exponent for space p. Express your answer in terms of ln space 7 and ln space 5.

How did you do?

Did this page help you?

5
Sme Calculator5 marks

Solve the equation 4 to the power of x minus 3 cross times 2 to the power of x plus 2 end exponent equals 64.

How did you do?

Did this page help you?

6
Sme Calculator5 marks

It is given that space p equals l o g subscript 124 125 cross times l o g subscript 123 124 cross times l o g subscript 122 123 cross times horizontal ellipsis cross times l o g subscript 5 6.

Given that space p element of straight integer numbers, find the value of space p.

How did you do?

Did this page help you?

7
Sme Calculator5 marks

Solve the equation  log subscript 6 3 plus log subscript 6 2 x equals 2 minus log subscript 6 12.

How did you do?

Did this page help you?

8
Sme Calculator5 marks

Solve the equation log subscript 9 x minus log subscript 9 2 equals 2 plus log subscript 9 5.

How did you do?

Did this page help you?

9a
Sme Calculator4 marks

Find the value of log subscript 4 32 plus log subscript 4 8.

How did you do?

9b
Sme Calculator4 marks

Find the value of 64 to the power of log subscript 4 3 end exponent.

How did you do?

Did this page help you?

10
Sme Calculator6 marks

Find the integer values of x andspace y for which x plus y space log subscript 9 5 plus 12 space log subscript 27 15 equals 0

How did you do?

Did this page help you?

1a
Sme Calculator2 marks

Let space f open parentheses x close parentheses space equals space ln space open parentheses x over 3 minus 1 close parentheses.

Find the values of x for whichspace f open parentheses x close parentheses is undefined.

How did you do?

1b
Sme Calculator3 marks

Given that point has A coordinates open parentheses a comma space 0 close parentheses, find the value of a.

How did you do?

Did this page help you?

2
Sme Calculator6 marks

Solve 27 to the power of 4 x plus 2 space end exponent equals space 81 to the power of 8 x minus 3 end exponent.

How did you do?

Did this page help you?

3
Sme Calculator6 marks

Solve 5 space ln space 2 space minus ln space 8 equals negative ln space x.

How did you do?

Did this page help you?

4
Sme Calculator6 marks

Solve the equation 216 to the power of k plus 2 end exponent space equals space 12 to the power of 3 k end exponent for k. Express your answer in terms of ln space 6 and ln space 2.

How did you do?

Did this page help you?

5
Sme Calculator5 marks

Solve the equation 2 cross times 25 to the power of x minus 30 cross times 5 to the power of x minus 1 end exponent equals 1.

How did you do?

Did this page help you?

6
Sme Calculator5 marks

It is given thatspace p space equals space log subscript 242 space 243 cross times log subscript 241 space 242 cross times log subscript 240 space 241 cross times... cross times log subscript 3 space 4.

Given thatspace p element of straight integer numbers comma find the value ofspace p.

How did you do?

Did this page help you?

7
Sme Calculator5 marks

Solve the equation log subscript 5 space end subscript x minus log subscript 5 space 4 space equals space 4 plus log subscript 5 space 2.

How did you do?

Did this page help you?

8
Sme Calculator7 marks

Solve the equation log subscript 4 space open parentheses 2 minus x close parentheses space equals space log subscript 16 space open parentheses 13 minus 4 x close parentheses.

How did you do?

Did this page help you?

9a
Sme Calculator4 marks

Find the value of log subscript 8 space 2560 minus log subscript 8 space end subscript 5.

How did you do?

9b
Sme Calculator4 marks

Find the value of 64 to the power of log subscript 8 space end subscript 5 end exponent.

How did you do?

Did this page help you?

10
Sme Calculator6 marks

Find the integer values of x and y for which x plus y space log subscript 343 space 6 minus 10 space log subscript 49 space 42 space equals space 0

How did you do?

Did this page help you?