Question

question 11 of 25
convert the following exponential equation to logarithmic form.
512 = 8³
options:
log₅₁₂(8) = 3
log₈(3) = 512
8 log(3) = 512
log₈(512) = 3

Explanation:

Step1: Recall the logarithm definition

The exponential form \( a^b = c \) converts to logarithmic form \( \log_a(c) = b \), where \( a>0,a
eq1 \).

Step2: Identify \( a \), \( b \), \( c \) in \( 512 = 8^3 \)

Here, \( a = 8 \), \( b = 3 \), \( c = 512 \).

Step3: Apply the conversion formula

Substitute into \( \log_a(c) = b \), we get \( \log_8(512) = 3 \).

Answer:

\(\log_{8}(512) = 3\) (the last option: \(\boldsymbol{\log_{8}(512) = 3}\))