Answered

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Which logarithmic equation is equivalent to [tex]$8^2=64$[/tex]?

A. [tex]2=\log_8 64[/tex]
B. [tex]2=\log_{64} 8[/tex]
C. [tex]8=\log_2 64[/tex]
D. [tex]64=\log_2 8[/tex]

Sagot :

GinnyAnswer
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]
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