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