Solve Log Equation - Precalculus & Trigonometry Step by Step

Solve log_2(x) = 4 by converting to exponential form: x = 2^4 = 16. Verify and check the domain x > 0.

Example: log_2(x) = 4 → x = 2^4 = 16. Verify: 2^4 = 16. Domain check: x = 16 > 0. ✓

Example

Rewrite the logarithmic equation in exponential form and check the domain.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

\log_{ 2 }(x)= 4

Step 2 — Exponential form

Exponentiate: x = 2^4.

x= \hl{2} ^{ \hl{4} }

Step 3 — Solve

Compute 2^4 = 16.

x= 2 ^{ 4 }= \hl{16}

Step 4 — Domain check

Check the log domain: x = 16 is greater than 0.

x= \hl{16} > \hl{0}

solve-log-equation To solve log_b(x) = k, convert to exponential form: x = b^k. Always check the domain: x must be positive (logarithms are undefined for non-positive arguments).