Free Printable H TEST (O) - 10.2-10.3 LOGS

1.

Solve each inequality.
$\log_7\left(x+2\right)\ge\log_7\left(6x\ -3\right)$

a)

$x\ \le1$

b)

$x\ >\ -2$

c)

$\frac{1}{2}\ <x\ \le1$

d)

x $x\ >\frac{1}{2}$

2.

a)

A

b)

B

c)

C

d)

D

3.

Solve: log₃x > 4

a)

x > 12

b)

x > 64

c)

x > 81

d)

x > 27

4.

SOLVE by using the properties

log (3x + 2) − log 5 = 2

a)

x = 3

b)

x = -5/21

c)

x = 0

d)

x = 166

5.

$\log_4x+\log_4\left(x-3\right)=1$ Solve the equation.

a)

$x=-4\ and\ x=1$

b)

$x=4$

c)

$x=1$

d)

$x=4\ and\ x=-1$

e)

$x=-1$

6.

log(2x) - log(5) = log(30)

a)

6/5

b)

45/2

c)

75

d)

-3/8

7.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

8.

Evaluate

log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

9.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

10.

Expand: log(3x)²

a)

2log(3+x)

b)

2log3+logx

c)

log3+2logx

d)

2(log3+logx)

11.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

12.

Use properties of Logs to write $\log_3\left(8\right)+\log_3\left(3\right)-\log_3\left(2\right)$

as one Log

a)

$\log_3\left(12\right)\$

b)

$\log_3\left(9\right)$

c)

$\log_3\left(48\right)$

d)

$\log_3\left(8\right)$

13.

Rewrite $11^2=121$ in logarithmic form.

a)

$\log_{11}121=2$

b)

$\log_2121=11$

c)

$\log_{11}2=121$

d)

$\log_211=121$

14.

Expand the logarithm
$\log_8\left(a^3b^4\right)$

a)

$3\log_8a+4\log_8b$

b)

$\log_{8\ }a^3+b^4$

c)

$\log_8a^3+\log_8b^4$

d)

$3\log_8a-4\log_8b$

15.

Condense into a single logarithm
$6\log_57-12\log_510$

a)

$\log_5\left(\frac{7^6}{10^{12}}\right)$

b)

$\log_5\left(7^6-10^{12}\right)$

c)

$\log_5\left(\frac{10^{12}}{7^6}\right)$

d)

$\log_5\left(7^6\cdot10^{12}\right)$

16.

Evaluate $\log_2\left(\frac{1}{8}\right)$

a)

$-3$

b)

$\frac{1}{3}$

c)

$\frac{1}{4}$

d)

$-4$

17.

$2\log3+4\log2=\ \log\$ (a)

Condense

18.

Condense

a)

A

b)

B

c)

C

d)

D

19.

Solve log₉ (x - 4) + log₉ (x + 1) = log₉ (x + 5) + log₉ (x - 6)

a)

17/2

b)

-9/16

c)

13

d)

-8

20.

$Use\ \log_{10}5\approx0.6990\ and\ \log_{10}7\approx0.8451\ to\ approximate\ \log_{10}175$

a)

2.2431

b)

2.8614

c)

1.3980

d)

1.5441

H TEST (O) - 10.2-10.3 LOGS

Total questions: 20

Worksheet time: 41mins

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