Which of the following is equivalent to (log_(b)(8))/(log_(b)(2)) ? Choose 1 answer: (A) 3 (B) 4 (C) log_(b)(3) (D) log(4)

Rewrite using change of base formula: Use the change of base formula for logarithms to rewrite the expression. Change of base formula: log_(a)(c) / log_(a)(b) = log_(b)(c) (log_(b)(8))/(log_(b)(2)) = log_(2)(8)Evaluate log_(2)(8): Evaluate log_(2)(8) knowing that 2^3 = 8. log_(2)(8) = log_(2)(2^3) = 3 * log_(2)(2)Simplify the expression: Simplify the expression using the fact that log_(b)(b) = 1. 3 * log_(2)(2) = 3 * 1 = 3

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Which of the following is equivalent to
(log_(b)(8))/(log_(b)(2)) ?
Choose 1 answer:
(A) 3
(B) 4
(C)
log_(b)(3)
(D)
log(4)

Which of the following is equivalent to $\frac{\log _{b}(8)}{\log _{b}(2)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $3$ $\newline$ (B) $4$ $\newline$ (C) $\log _{b}(3)$ $\newline$ (D) $\log (4)$

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Math Problems

Algebra 2

Product property of logarithms

Full solution

Q. Which of the following is equivalent to

\frac{\log _{b}(8)}{\log _{b}(2)}

\newline

Choose

1

answer:

\newline

(A)

3

\newline

(B)

4

\newline

(C)

\log _{b}(3)

\newline

(D)

\log (4)

Rewrite using change of base formula: Use the change of base formula for logarithms to rewrite the expression. $\newline$ Change of base formula: $\log_{a}(c) / \log_{a}(b) = \log_{b}(c)$ $\newline$ $(\log_{b}(8))/(\log_{b}(2)) = \log_{2}(8)$
Evaluate $\log_{2}(8)$ : Evaluate $\log_{2}(8)$ knowing that $2^3 = 8$ . $\newline$ $\log_{2}(8) = \log_{2}(2^3) = 3 \cdot \log_{2}(2)$
Simplify the expression: Simplify the expression using the fact that $\log_{b}(b) = 1$ . $\newline$ $3 \times \log_{2}(2) = 3 \times 1 = 3$