Question

12 change to exponential form: \\(\log_{5} (125) = 3\\) \\(\boldsymbol{a}\\) \\(5^3 = 125\\) \\(\boldsymbol{b}\\) \\(125^5 = 3\\) \\(\boldsymbol{c}\\) \\(125^3 = 5\\) \\(\boldsymbol{d}\\) \\(3^5 = 125\\)

Explanation:

Step1: Recall logarithm to exponential conversion

The logarithmic form \( \log_b(a) = c \) converts to the exponential form \( b^c = a \).

Step2: Identify \( b \), \( a \), \( c \) in \( \log_5(125) = 3 \)

Here, \( b = 5 \), \( a = 125 \), \( c = 3 \).

Step3: Apply the conversion formula

Substitute into \( b^c = a \), we get \( 5^3 = 125 \).

Answer:

A. \( 5^3 = 125 \)