Free Practice Quiz Question List

11/14 11. Logarithmic Functions and Equations Online Quiz Questions

Use this free practice quiz with 20 questions to review 11/14 11. Logarithmic Functions and Equations, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which condition must the argument of a logarithm satisfy for the logarithm to be defined?

A
The argument may be any real number.
B
The argument must be positive.
C
The argument must be greater than 1.
D
The argument must be nonzero, but it may be negative.

True or false

1 point

True or false: $\ln(x)$ denotes a logarithm with base $e$ .

A
True
B
False

Choose one

1 point

What is the vertical asymptote of $f(x)=\log_3(x-2)+1$ ?

A
$x=0$
B
$x=-2$
C
$x=2$
D
$x=1$

Written response

1 point

Solve $\log_3(2x-1)=4$ . Enter the value of $x$ .

Fill in the blank

1 point

Complete the definition of a logarithm: $\log_b(x)=y$ is equivalent to = x.

True or false

1 point

True or false: For positive values where the expressions are defined, $\log_b(x+y)=\log_b(x)+\log_b(y)$ .

A
True
B
False

Choose all

1 point

Which statements are valid logarithm properties for positive quantities and a valid base? Select all correct choices.

A
$\log_b(MN)=\log_b(M)+\log_b(N)$
B
$\log_b\left(\frac{M}{N}\right)=\log_b(M)-\log_b(N)$
C
$\log_b(M+N)=\log_b(M)+\log_b(N)$
D
$\log_b(M^p)=p\log_b(M)$

Written response

1 point

Solve $\log_2(x)+\log_2(x-2)=3$ . Enter the valid value of $x$ .

Choose one

1 point

Which expression correctly applies the change-of-base formula to $\log_5(17)$ ?

A
$\frac{\ln(5)}{\ln(17)}$
B
$\frac{\ln(17)}{\ln(5)}$
C
$\ln(17)-\ln(5)$
D
$\frac{17}{5}$

Choose all

1 point

Which characteristics belong to the parent function $y=\log_b(x)$ , where $b>0$ and $b\neq 1$ ? Select all correct choices.

A
Its domain is $(0,\infty)$ .
B
Its range is all real numbers.
C
It has a y-intercept at $(0,1)$ .
D
Its vertical asymptote is $x=0$ .

Open ended

1 point

Solve $\log_2(x)+\log_2(x-2)=3$ . Show how the domain restriction is used to identify and reject any extraneous solution.

Choose one

1 point

Solve $\log_5(x+1)=2$ . Which value of $x$ satisfies the original equation?

A
$x=4$
B
$x=20$
C
$x=24$
D
$x=26$

Fill in the blank

1 point

For $f(x)=a\log_b(x-h)+k$ , complete the domain condition: .

Written response

1 point

Rewrite the exponential statement $4^3=64$ in logarithmic form.

Choose one

1 point

What is the domain of $f(x)=\log_2(x-4)-3$ ?

A
$x<4$
B
$x\geq 4$
C
$x>4$
D
All real numbers

Choose one

1 point

Which expression correctly expands $\log_b\left(\frac{x^2}{y^3}\right)$ , assuming $x>0$ and $y>0$ ?

A
$2\log_b(x)-3\log_b(y)$
B
$2\log_b(x)+3\log_b(y)$
C
$\log_b(x)-\log_b(y)$
D
$\log_b(x^2-y^3)$

Choose one

1 point

Solve $\log_4(x-1)=2$ .

A
3
B
4
C
15
D
17

Choose one

1 point

Which statement correctly describes the graph of $y=\log_{1/2}(x)$ ?

A
It is increasing because the base is positive.
B
It is decreasing because the base is between 0 and 1.
C
It is constant because logarithms are inverse functions.
D
It has no real domain because the base is less than 1.

True or false

1 point

True or false: In a real logarithmic expression, the argument of every logarithm may be zero as long as the base is valid.

A
True
B
False

Written response

1 point

What is the name of a logarithm with base $e$ ?