Free Printable G10AP QZ.10 Solving Logarithmic Equations and Inequalities

1.

Solve log₅(4x-7)=log₅(x+5).

a)

x=4

b)

x=-4

c)

x=3

d)

x=-2

2.

a)

A

b)

B

c)

C

d)

D

3.

a)

A

b)

B

c)

C

d)

D

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

Solve the equation.

$\ln\left(x-4\right)^5=35$

a)

$\ln\left(\frac{39}{5}\right)$

b)

$e^7-4$

c)

$e^7+4$

d)

$e^4-7$

7.

Which of these statements are true corresponding to this equation? Check ALL that apply.
$e^{\left(\frac{x}{3}+2\right)}-1=7$

a)

$\frac{x}{3}+2=\ln8$

b)

$x=6\ln8-3$

c)

$x=3\left(\ln8-2\right)$

d)

$x=3\ln8-6$

e)

$\frac{x}{3}=\ln4$

8.

What is the solution set for the inequality
log (2x – 1) < log (5 – 3x)?

a)

$\frac{1}{2}<x\ <\frac{4}{5}$

b)

$\frac{1}{2}<\ x\ <\ \frac{6}{5}$

c)

$\frac{1}{2\ }<\ x\ <\ \frac{5}{3}$

d)

$\frac{6}{5}<\ x\ <\frac{5}{3}$

9.

What is the solution set of this equation? $\log_3\left(x^2\ -\ 16\right)\ =\ \log_36x\$

a)

{- 2 ; 8}

b)

{ 8 }

c)

no solution

d)

{ -2 }

10.

$\log_{4\ }x^2\ =\ \log_4\ x$
How many solutions are there to the following problem?

a)

1

b)

0

c)

2

d)

3

11.

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

G10AP QZ.10 Solving Logarithmic Equations and Inequalities

Total questions: 11

Worksheet time: 30mins

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