State the domain, then combine logarithms of the same base.
\(\log_a M=\log_a N\iff M=N\)
\(\log_a M=k\iff M=a^k\)
Here \(a>0,\ a\ne1\) and \(M,N>0\).
Reject any root that makes an original argument non-positive or a base invalid.
Exponential equations
\(a^x=b\quad\Longrightarrow\quad x=\dfrac{\ln b}{\ln a}\quad(a>0,\ a\ne1,\ b>0)\)
\(3^x=20\quad\Longrightarrow\quad x=\) \(\quad(3\text{ s.f.})\)
For equations in \(a^{2x}\) and \(a^x\), let \(u=a^x>0\). Solve the quadratic in \(u\), then find \(x\).
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