Exponential & Logarithmic Practice
Read the exponent: evaluate powers, solve b^x = v, flip log form both ways, and expand/condense with the log laws.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
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Problem
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Evaluate powers
b^x, including negatives.
2^(−3) = 1/8
Solve b^x = v
Read the exponent.
3^x = 81 → 4
Evaluate logs
log_b(x): which power?
log₅(125) = 3
Solve log equations
Flip to b^e = x.
log₂(x) = 6 → 64
Expand
Power law outward.
log₂(x³y²) → …
Condense
Laws in reverse.
2log₃x + 3log₃y → …
Exponential models
f(t) = a·b^t.
a·b^t at t = ?
Log domain
x > 0 always.
domain of log_b(x)
3 Watch out for these
The three mistakes students make most often on these problems.
Logs split products, not sums
log(x + y) does NOT equal log x + log y.
x must be positive
log_b of zero or a negative is undefined.
Exponents are not division
2^x = 16 → x = 4, not 16/2.