Which of the following is equivalent to log_(4)(m)*log_(m)(20) ? Choose 1 answer: (A) 5 (B) 80 (C) log(5) (D) log_(4)(20)

Use Change of Base Formula: We will use the change of base formula for logarithms, which states that log_(a)(b) * log_(b)(c) = log_(a)(c). This is because log_(a)(b) is the exponent to which 'a' must be raised to get 'b', and log_(b)(c) is the exponent to which 'b' must be raised to get 'c'. When you multiply these, you get the exponent to which 'a' must be raised to get 'c'.Apply Change of Base Formula: Applying the change of base formula to log_(4)(m)*log_(m)(20), we get: log_(4)(m)*log_(m)(20) = log_(4)(20)Check Answer Choices: Now we need to check the answer choices to see which one matches log_(4)(20). The correct answer should be (D) log_(4)(20), as it is the direct result of applying the change of base formula.

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Which of the following is equivalent to
log_(4)(m)*log_(m)(20) ?
Choose 1 answer:
(A) 5
(B) 80
(C)
log(5)
(D)
log_(4)(20)

Which of the following is equivalent to $\newline$ $\log_{4}(m)\cdot\log_{m}(20)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $5$ $\newline$ (B) $80$ $\newline$ (C) $\log(5)$ $\newline$ (D) $\log_{4}(20)$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which of the following is equivalent to

\newline

\log_{4}(m)\cdot\log_{m}(20)

\newline

Choose

1

answer:

\newline

(A)

5

\newline

(B)

80

\newline

(C)

\log(5)

\newline

(D)

\log_{4}(20)

Use Change of Base Formula: We will use the change of base formula for logarithms, which states that $\log_{a}(b) \cdot \log_{b}(c) = \log_{a}(c)$ . This is because $\log_{a}(b)$ is the exponent to which 'a' must be raised to get 'b', and $\log_{b}(c)$ is the exponent to which 'b' must be raised to get 'c'. When you multiply these, you get the exponent to which 'a' must be raised to get 'c'.
Apply Change of Base Formula: Applying the change of base formula to $\log_{4}(m)\cdot\log_{m}(20)$ , we get: $\newline$ $\log_{4}(m)\cdot\log_{m}(20) = \log_{4}(20)$
Check Answer Choices: Now we need to check the answer choices to see which one matches $\log_{4}(20)$ . The correct answer should be (D) $\log_{4}(20)$ , as it is the direct result of applying the change of base formula.