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The function
f is given by
f(x)=log_(2)x. What input value in the domain of
f yields an output value of 4 ?
(A) 32

f(x)=log_(2)x
(B) 16
(C) 2

log_(2)8=3
(D)
(1)/(2)

log_(2)x=4quad2^(3)=8

The function $f$ is given by $f(x)=\log _{2} x$ . What input value in the domain of $f$ yields an output value of $4$ ? $\newline$ (A) $32$ $\newline$ $f(x)=\log _{2} x$ $\newline$ (B) $16$ $\newline$ (C) $2$ $\newline$ $\log _{2} 8=3$ $\newline$ (D) $\frac{1}{2}$ $\newline$ $\log _{2} x=4 \quad 2^{3}=8$

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Quotient property of logarithms

Full solution

Q. The function

f

is given by

f(x)=\log _{2} x

. What input value in the domain of

f

yields an output value of

4

?

\newline

(A)

32

\newline

f(x)=\log _{2} x

\newline

(B)

16

\newline

(C)

2

\newline

\log _{2} 8=3

\newline

(D)

\frac{1}{2}

\newline

\log _{2} x=4 \quad 2^{3}=8

Identify equation: Identify the equation to solve: $f(x) = \log_2(x) = 4$ . We need to find $x$ such that the logarithm base $2$ of $x$ equals $4$ .
Convert to exponential form: Convert the logarithmic equation to its exponential form to solve for $x$ : $2^4 = x$ .
Calculate value: Calculate the value of $2^4$ : $2^4 = 16$ .

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