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Rewrite the following in the form
log(c).

4log(5)

Rewrite the following in the form $\log (c)$ . $\newline$ $4 \log (5)$

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Evaluate logarithms using properties

Full solution

Q. Rewrite the following in the form

\log (c)

.

\newline

4 \log (5)

Given expression: We are given the expression $4\log(5)$ and we need to rewrite it in the form $\log(c)$ . To do this, we can use the power property of logarithms, which states that $n \cdot \log_b(a) = \log_b(a^n)$ . We will apply this property to the given expression.
Applying power property: Using the power property, we rewrite $4\log(5)$ as $\log(5^4)$ . This is because multiplying a logarithm by a number is the same as raising the logarithm's argument to the power of that number.
Rewriting using power property: Now we calculate $5^4$ to find the value of $c$ . The calculation is as follows: $5 \times 5 \times 5 \times 5 = 625$ .
Calculating the value of $c$ : We substitute the value we found back into the logarithmic expression. So, $\log($ $5$ ^ $4$ ) becomes $\log($ $625$ ).
Substituting the value back: We have successfully rewritten the expression $4\log(5)$ in the form $\log(c)$ , where $c$ is $625$ .

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