Question

Rewrite 53 = 125 as a logarithmic equation.

A. Logv3 125 = 5
B. Logv5 125 = 3
C. Logv125 3 = 5
D. Logv5 3 = 125

Answer 1

To rewrite the equation \(53 = 125\) as a logarithmic equation, we can first express it in the form \(b^y = x\), where \(b\) is the base, \(y\) is the exponent, and \(x\) is the result.

Here, \(5^3 = 125\). To express this in logarithmic form, we can use the logarithm definition:

\[
\log_b(x) = y \quad \text{is equivalent to} \quad b^y = x
\]

From the equation \(5^3 = 125\), we can convert it to logarithmic form:

\[
\log_5(125) = 3
\]

Now we can match this with the answer options provided:

A. \( \log_3(125) = 5 \)

B. \( \log_5(125) = 3 \) **(This is correct)**

C. \( \log_{125}(3) = 5 \)

D. \( \log_5(3) = 125 \)

The correct answer is:

**B. \(\log_5(125) = 3\)**