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Which of the following is equivalent to
(log_(c)(6))/(log(6)) ?
Choose 1 answer:
(A)
log(c)
(B)
log_(c)(1)
(c)
(1)/(log(c))
(D)
(1)/(log(6))

Which of the following is equivalent to $\frac{\log _{c}(6)}{\log (6)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\log (c)$ $\newline$ (B) $\log _{c}(1)$ $\newline$ (C) $\frac{1}{\log (c)}$ $\newline$ (D) $\frac{1}{\log (6)}$

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Product property of logarithms

Full solution

Q. Which of the following is equivalent to

\frac{\log _{c}(6)}{\log (6)}

?

\newline

Choose

1

answer:

\newline

(A)

\log (c)

\newline

(B)

\log _{c}(1)

\newline

(C)

\frac{1}{\log (c)}

\newline

(D)

\frac{1}{\log (6)}

Given Expression: We are given the expression $(\log_{c}(6))/(\log(6))$ and we need to find an equivalent form among the given options. We can use the change of base formula for logarithms, which states that $\log_{a}(b) = \log(c)(b) / \log(c)(a)$ for any positive numbers $a$ , $b$ , and $c$ (where $a \neq 1$ and $c \neq 1$ ). We will apply this formula to the given expression.
Apply Change of Base Formula: Using the change of base formula, we can rewrite the given expression as follows: $\newline$ $\frac{\log_{c}(6)}{\log(6)} = \frac{\log(6) / \log(c)}{\log(6)}$
Simplify the Expression: We can simplify the expression by dividing $\log(6)$ by itself, which equals $1$ : $\frac{\log(6)}{\log(c)} / \log(6) = \frac{1}{\log(c)}$
Compare with Options: Now we compare the simplified expression with the given options. The expression $\frac{1}{\log(c)}$ matches option (C), which is $\frac{1}{\log(c)}$ .
Final Equivalent Form: We have found the equivalent form without any mathematical errors, and it matches one of the given options.

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