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Which of the following is equivalent to
(1)/(log_(b)(4)) ?
Choose 1 answer:
(A)
log_(b)(4)
(B)
log_(4)(b)
(c)
-log_(b)(4)
(D)
-log_(4)(b)

Which of the following is equivalent to $\frac{1}{\log _{b}(4)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\log _{b}(4)$ $\newline$ (B) $\log _{4}(b)$ $\newline$ (C) $-\log _{b}(4)$ $\newline$ (D) $-\log _{4}(b)$

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Product property of logarithms

Full solution

Q. Which of the following is equivalent to

\frac{1}{\log _{b}(4)}

?

\newline

Choose

1

answer:

\newline

(A)

\log _{b}(4)

\newline

(B)

\log _{4}(b)

\newline

(C)

-\log _{b}(4)

\newline

(D)

-\log _{4}(b)

Recognize relationship between reciprocal and change of base formula: Recognize the relationship between the reciprocal of a logarithm and the change of base formula. $\newline$ The reciprocal of a logarithm, such as $(1)/(\log_{b}(4))$ , can be related to the change of base formula for logarithms. $\newline$ Change of Base Formula: $\log_{a}(c) = (\log_{b}(c)) / (\log_{b}(a))$ $\newline$ We need to find an expression that represents the reciprocal of $\log_{b}(4)$ in terms of another logarithm.
Apply change of base formula to given expression: Apply the change of base formula to the given expression. $\newline$ We want to express $(1)/(\log_{b}(4))$ using the change of base formula. To do this, we need to find a logarithm whose base is $4$ and argument is $b$ , because the change of base formula would then give us: $\newline$ $\log_{4}(b) = (\log_{b}(b)) / (\log_{b}(4))$ $\newline$ Since $\log_{b}(b) = 1$ , we have: $\newline$ $\log_{4}(b) = 1 / (\log_{b}(4))$ $\newline$ This matches the given expression $(1)/(\log_{b}(4))$ .

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