Worksheets — Solving Logarithmic Equations

Solve for $x$ in each of the following:
(a) $\log_2(2x - 3) = 3$     (b) $\log_5(x) = 2$     (c) $\log_x(16) = 2$

Find the value of $x$ (equate arguments directly):
$\log(3x - 4) = \log(5)$

Verify whether $x = -2$ is a valid solution for $\log_3(x + 5) = 1$. Show your steps.

Solve for $x$ and check for extraneous roots:
$\log_3(x) + \log_3(x - 8) = 2$

Solve the quadratic logarithmic equation:
$(\log_2 x)^2 - 5\log_2 x + 6 = 0$

Find all real solutions for $x$:
$\log_2(x^2 - 7) = 3$

Solve for $x$ in the nested equation:
$\log_3(\log_2 x) = 1$

Solve for $x$ if base is a variable:
$\log_x(3x + 10) = 2$

Find $x$ in the exponential-logarithmic hybrid equation:
$1000^{\log_{10} x} = 8$