Solving logarithmic equations by converting to exponential form or using properties, checking for extraneous solutions, and solving any exponential equation with logarithms.
Logarithmic equations
Exponential equations with any base
Logarithms let you solve any exponential equation, even when the bases don't match: isolate the power, then take a logarithm of both sides.
Practice
Quick check
What is the solution of \(\log_2 x = 5\)?
\(x = 2^5 = 32\).
Quick check
Solving \(\log(x) + \log(x + 1) = \log 6\), you get \(x = 2\) and \(x = -3\). Which are solutions?
\(\log(-3)\) is undefined, so \(x = -3\) is extraneous.
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