Exponential and Logarithmic Equations and Inequalities

What AP Precalc asks here

Exponential equations are usually solved by rewriting both sides to a common base (then equating exponents) or by taking a log of both sides. Log equations are solved by exponentiating to remove the log, but every candidate must be checked: a value that makes any log argument non-positive is extraneous. Some mixed equations like $b^{2x} - cb^x + d = 0$ yield to the substitution $u = b^x$.

Rewrite both sides to a common base if possible; otherwise take a log of both sides.

Combine logs, exponentiate, solve the resulting polynomial, then verify each candidate makes the original log arguments positive.

Substitute $u = b^x$ in mixed exponential equations. For inequalities, isolate, exponentiate, and preserve direction when $b > 1$.