Free Printable Logarithms Review

1.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

2.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

Rewrite x^p = m in logarithmic form.

a)

log_xp = m

b)

log_mx = p

c)

log_xm = p

d)

log_pm = x

5.

Evaluate the following logarithm:
$\log_416$

a)

1

b)

-2

c)

2

d)

¹/₂

6.

Evaluate the following logarithm:
$\log_327$

a)

3

b)

2

c)

9

d)

$\frac{1}{3}$

7.

Evaluate the following logarithm:
$\log_55$

a)

1

b)

0

c)

-1

d)

¹/₂

8.

Evaluate the following logarithm:
$\log_{49}7$

a)

¹/₇

b)

-2

c)

2

d)

¹/₂

9.

Expand $\log(x^7)$

a)

$\log(7x)$

b)

$\log7+\log x$

c)

$x\log7$

d)

$7\log x$

10.

Expand:

$\log\left(\frac{m^3}{n}\right)$

a)

$\log m-\log3-\log n$

b)

$3\log m+\log n$

c)

$3\log m-\log n$

d)

$3\log(m-n)$

11.

Expand the logarithm:
$\log\left(x\cdot y\right)$

(a)

12.

Expand the logarithm:
$\log\left(\frac{x}{y}\right)$

(a)

13.

a)

$\log(xy^3)$

b)

$\log(x^6−y^3)$

c)

$\log\left(\frac{x^6}{y^3}\right)$

d)

$\log(x^6+y^3)$

14.

Condense

a)

$\log\left(xyz^3\right)$

b)

$\log\left(\frac{xy}{z^3}\right)$

c)

$\log x+\log y+\log z^3$

d)

$\log\left(x^3y^3z^3\right)$

15.

Write as one logarithm. Simplify, if possible.

$\log_2800-\log_2100$

a)

8

b)

3

c)

-3

d)

1

16.

Write as one logarithm. Simplify, if possible.

$\log_37.5+\log_31.2$

a)

8.7

b)

2

c)

3

d)

6.25

17.

Solve the equation

$5^{x-2}=20$

a)

$\frac{2\log5}{\log20}$

b)

$\frac{\log20}{\log5}+2$

c)

$\log\left(4\right)+2$

d)

$\log6$

18.

Solve the equation, round to the nearest hundredth.

$5^{x-2}=20$

(a)

19.

Solve the equation:

$6^{3x-5}=15$

a)

$\frac{1}{3}\left(\log\left(\frac{15}{6}\right)+5\right)$

b)

$3\left(\log\left(15\right)-\log\left(6\right)-5\right)$

c)

$\frac{1}{3}\left(\frac{\log15}{\log6}+5\right)$

d)

$3\left(\frac{\log6}{\log15}\right)-5$

20.

Solve the equation, round to the nearest hundredth.

$6^{3x-5}=15$

(a)

21.

The population of a town is increasing, modeled by the function:
$p\left(t\right)=20,000\left(1.05\right)^t$
After how many years will the population reach 27,000? Round to the nearest hundredth.

(a)

22.

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.
The relationship between the elapsed time t, in minutes, and the number of bacteria, B(t), in the Petri dish is modeled by the following function.
$B\left(t\right)=10\left(2\right)^{\frac{t}{15}}$
After how many minutes will there be 120 bacteria? Round your answer to the nearest hundredth.

(a)

23.

Solve the equation:
$e^{3x}=12$

a)

$\frac{\ln12}{3}$

b)

$\ln4$

c)

$\frac{e^{12}}{3}$

d)

$\frac{\ln12}{\ln3}$

24.

Solve the equation:
$e^{3x}=12$
Round to the nearest hundredth.

(a)

25.

What kind of asymptotes do logs have?

a)

horizontal ( y=0)

b)

vertical (x=0)

26.

find the asymptote: y = log₁₀ (x+3) - 5

a)

$x=-3$

b)

$y=3$

c)

$x=-5$

d)

$y=5$

27.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=(x+6)log3+4

28.

Describe the transformations of:
$f\left(x\right)=-\log_2\left(x+1\right)$

a)

left one & y-axis reflection

b)

right one & y-axis reflection

c)

left one & x-axis reflection

d)

right one & x-axis reflection

29.

Match the graph with its equation

a)

$y=-\log_6(x)+2$

b)

$y=\log_6(x−2)+1$

c)

$y=\log_6(x+2)-1$

30.

Select the equation of the function shown

a)

$f\left(x\right)=\log_3\left(x-4\right)-1$

b)

$f\left(x\right)=-\log_3\left(x-4\right)+1$

c)

$f\left(x\right)=\log_3\left(x+4\right)-1$

d)

$f\left(x\right)=-3^{x+4}$

31.

Describe domain of the function shown

a)

$\left(-\infty,\infty\right)$

b)

$\left(-4,\infty\right)$

c)

$\left(-\infty,-4\right)$

d)

$\left(-\infty,2\right)$

32.

Select the graph of the function:
$f\left(x\right)=\log_4\left(x-3\right)-5$

a)

b)

c)

d)

33.

Select the graph of the function:
$f\left(x\right)=-\log_5\left(x+4\right)$

a)

b)

c)

d)

Logarithms Review

Total questions: 33

Worksheet time: 1hrs 1mins

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