Free Printable Indices and Logarithms

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Indices and Logarithms

Total questions: 16

Worksheet time: 44mins

Name

Class

Date

Solve log₂₇[log₃(5x+2)]=log₈2

Given y=log₃5. find the value of 9^y. Then, if x = y+2, find 9^x.

9^y=5 and 9^x=405

9^y=25 and 9^x=2025

9^y=20 and 9^x=1620

9^y=10 and 9^x=810

Solve 2^log₃^x=16

Solve 2^x+3=14+2^x

If 2-log₁₀x=3log₁₀y, express x in terms of y.

10y³

10/y³

100/y³

100y³

Solve 9^2x=1/243

-4/5

5/4

4/5

-5/4

Solve log_√x64-log_√x2=5

Solve log₂x+log₄2x=-1

1/2

Solve √(27^x+4)=1/(3^x+39^x)

-9

-2

10.

Simplify 3ⁿ⁺³-3ⁿ+6(3^n-1)

10(3ⁿ)

27(3ⁿ)

28(3ⁿ)

9(3ⁿ)

11.

Solve 9^log₃^x=7

0.6946

2.6458

0.8870

3.0886

12.

Solve 3^x4^x=7^x+1

1.6012

3.6102

2.5613

0.8451

13.

Given log_√x8=p and log_y2=q. Write log₈x²y in terms of p and q.

(12q+p)/(3pq)

(4q+1)/(3pq)

(4q+1)/(3q)

(7q+p)/(3q)

14.

Given log_m2=x and log_m6=y. Express log_m(24/m⁴) in terms of x and y.

y+4x-4

4y+x-4

2x+y-4

x+2y-4

15.

Given 32(4^x+2)=2^y and log₃y=2+log₃(x+1). Find the value of x and y.

x=72 ; y=7

x=7 ; y=72

x=9 ; y=0

x=0 ; y=9

16.

Given that log_h2=0.6312, solve √2 × h^x+1=2.

1.3156

-0.6844

0.3156

1.2624

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Indices and Logarithms

Total questions: 16

Worksheet time: 44mins

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