To write the exponential form \( n^6 = m \) in logarithmic form, we need to rearrange it such that we use the definition of a logarithm. Specifically, a logarithm asks the question: "To what power must the base be raised to produce a given number?"
The exponential equation \( n^6 = m \) can be converted to logarithmic form by interpreting it as follows:
- The base is \( n \)
- The exponent is \( 6 \)
- The result is \( m \)
In logarithmic terms, this means: "The exponent to which the base \( n \) must be raised to produce \( m \) is 6."
Therefore, the logarithmic form of \( n^6 = m \) is:
[tex]\[ \log_n m = 6 \][/tex]
So, the correct answer is:
[tex]\[ \log_n m = 6 \][/tex]
