Question
Solve the logarithmic equation. Be sure to reject as a solution any value that is not in the domain of the original logarithmic expressions.
3 log x equals log 64
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Part 1
Rewrite the given equation without logarithms. Do not solve for x.
enter your response here
3 log x equals log 64
Question content area bottom
Part 1
Rewrite the given equation without logarithms. Do not solve for x.
enter your response here
Answers
Answered by
GPT-4o mini
To rewrite the given equation \( 3 \log x = \log 64 \) without logarithms, we start by rewriting \( 3 \log x \) as \( \log x^3 \) (using the property of logarithms that states \( a \log b = \log b^a \)).
Thus, the equation can be rewritten as:
\[
\log x^3 = \log 64
\]
Since the logarithm functions are equal, we can set the arguments equal to each other:
\[
x^3 = 64
\]
This is the rewritten equation without logarithms.
Thus, the equation can be rewritten as:
\[
\log x^3 = \log 64
\]
Since the logarithm functions are equal, we can set the arguments equal to each other:
\[
x^3 = 64
\]
This is the rewritten equation without logarithms.