To determine which logarithmic equation is equivalent to \( 8^2 = 64 \), we need to utilize the relationship between exponents and logarithms. The definition of a logarithm states that if \( a^b = c \), then \( \log_a(c) = b \).
Given the equation \( 8^2 = 64 \):
- \( a \) is the base, which is \( 8 \).
- \( b \) is the exponent, which is \( 2 \).
- \( c \) is the result, which is \( 64 \).
Using the logarithmic form, we can rewrite this as:
[tex]\[ \log_8 64 = 2 \][/tex]
Therefore, the correct logarithmic equation that is equivalent to \( 8^2 = 64 \) is:
[tex]\[ 2 = \log _8 64 \][/tex]
