[tex]\operatorname{\log}_a5.8=7[/tex]
1) Note that since we cannot reduce both sides of that equality to the same base, one way to rewrite it is to resort to a logarithm.
The Definition of a Logarithm is:
[tex]\log_ab=c\Leftrightarrow a^c=b[/tex]
2) Now, we can rewrite that exponential statement as a logarithm that way:
[tex]\begin{gathered} a^7=5.8 \\ \log_aa^7=\log_a5.8 \\ \log_a5.8=7\Leftrightarrow a^7=5.8 \\ \log_a5.8=7 \end{gathered}[/tex]
Note that whenever the base of a logarithm is the same as the exponent of its argument we can tell that log is equal to its exponent.
