Answer:
[tex]x = \log_b y[/tex]
Step-by-step explanation:
Using logarithmic rules:
[tex]\log a^x = x \log a[/tex]
[tex]\frac{\log x}{\log b} = \log_b x[/tex]
Given the equation:
[tex]y = b^x[/tex]
Taking log both sides we have;
[tex]\log y = \log b^x[/tex]
Apply the logarithmic rule:
[tex]\log y = x \log b[/tex]
Divide both sides by log b we have;
[tex]\frac{\log y}{\log b} = x[/tex]
Apply the logarithmic rule:
[tex]\log_b y = x[/tex]
or
[tex]x = \log_b y[/tex]
Therefore, the equation in logarithmic form is, [tex]x = \log_b y[/tex]
