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Which of the following is the best first step in solving the equation below?

[tex]4 \log _5 x = 28[/tex]

A. [tex]\log 4 + \log _5 x = \log 7[/tex]
B. [tex]\log _5 x^4 = 7[/tex]
C. [tex]\log _5 x = 7[/tex]
D. [tex]4 x = 5^{28}[/tex]

Answer :

To solve the equation [tex]\( 4 \log_5 x = 28 \)[/tex], the best first step is to isolate [tex]\(\log_5 x\)[/tex]. Here's how you do it step by step:

1. Start with the original equation:
[tex]\[
4 \log_5 x = 28
\][/tex]

2. Divide both sides of the equation by 4 to isolate [tex]\(\log_5 x\)[/tex]:
[tex]\[
\log_5 x = \frac{28}{4}
\][/tex]

3. Simplify the right side:
[tex]\[
\log_5 x = 7
\][/tex]

This shows that option C, [tex]\(\log_5 x = 7\)[/tex], is the correct first step in solving the equation. Once you have [tex]\(\log_5 x = 7\)[/tex], you can proceed to find [tex]\(x\)[/tex] by changing the logarithmic equation into its exponential form.

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