Free Printable U3:L2-5 Exponent and Logarithm Review

1.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

2.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

3.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

4.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

5.

Solve $\log_6x+\log_69=\log_654$

a)

x=6

b)

x=45

c)

x=7

d)

x=36

6.

Solve $\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$

a)

$x=\frac{3}{4}$

b)

$x=3$

c)

$x=6$

d)

$x=\frac{4}{3}$

7.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

8.

Solve

a)

1/2

b)

-1/2

c)

2

d)

-2

9.

Solve

a)

1/3

b)

-1/3

c)

-3

d)

3

10.

Expand: log₂x⁶

a)

xlog₂6

b)

log₂x - log₂6

c)

log₂x + log₂6

d)

6log₂x

11.

Expand: log₅8x

a)

xlog₅8

b)

log₅8 + log₅x

c)

log₅8 - log₅x

d)

8log₅x

12.

Expand:

a)

log₆y - log₆2

b)

log₆y + log₆2

c)

2log₆y

d)

ylog₆2

13.

Expand:

a)

3log₅7x

b)

3log₅x + log₅7

c)

log₅7 - 3log₅x

d)

3log₅x - log₅7

14.

Expand: log₈6x³y

a)

log₈6 + log₈x - 3log₈y

b)

3log₈6 - log₈x + log₈y

c)

log₈6 + 3log₈x - log₈y

d)

log₈6 + 3log₈x + log₈y

15.

Condense: 5log₈y

a)

log₈5^y

b)

$\log_8\left(\frac{y}{5}\right)$

c)

log₈5y

d)

log₈y⁵

16.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

17.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

18.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

19.

Write the equation in logarithmic form. $27^{\frac{2}{3}}=9$

a)

$\log_{\frac{2}{3}}9=27$

b)

$\log_{27}\frac{2}{3}=9$

c)

$\log_{27}9=\frac{2}{3}$

d)

$\log_927=\frac{2}{3}$

20.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

21.

Which exponential expression is equivalent to $x^{12}$ ?

a)

$\frac{x^3}{x^4}$

b)

$\frac{x^4}{x^{-8}}$

c)

$\frac{x^4}{x^8}$

d)

$x^{-12}$

22.

Which exponential expression is equivalent to $x^9$ ?

a)

$x^2\cdot x^9$

b)

$x\cdot x^9$

c)

$x^3\cdot x^3$

d)

$x^5\cdot x^4$

23.

Which exponential expression is equivalent to $\frac{1}{x^{10}}$ ?

a)

$\frac{x^5}{x^5}$

b)

$x^5\cdot x^2$

c)

$x^2\cdot x^8$

d)

$\left(x^{-2}\right)^5$

24.

Which exponential expression is equivalent to $\frac{1}{x^8}$ ?

a)

$x^2\cdot x^6$

b)

$x^{-8}$

c)

$x^8$

d)

$\left(x^2\right)^4$

25.

2log (2x)⁴ = 16

a)

x = 4

b)

x = 10

c)

x = 50

d)

x = 2

U3:L2-5 Exponent and Logarithm Review

Total questions: 25

Worksheet time: 1hrs 20mins

Similar Resources on Wayground