Worksheets — Logarithmic Laws & Properties

Express as a single logarithm:
(a) $\log(5) + \log(6)$     (b) $\log_2(24) - \log_2(8)$     (c) $2\log_3(4)$

Simplify using power properties:
(a) $\log_5(125) - \log_5(5)$     (b) $\frac{1}{3}\log_2(64)$

Evaluate the exact value of:
(a) $\log(100) + \log(10)$     (b) $\log_2(16) \cdot \log_3(3)$

Given $\log(2) = x$ and $\log(3) = y$, write the following in terms of $x$ and $y$:
(a) $\log(6)$     (b) $\log(1.5)$     (c) $\log(12)$

Evaluate using the Change of Base Formula:
(a) $\log_9(27)$     (b) $\log_8(16)$     (c) $\log_4(32)$

Express as a single logarithm:
(a) $2 + \log(3)$     (b) $3\log_2(5) - 2$

Prove that for any positive base $a \neq 1$, $\log_a(x) \cdot \log_x(a) = 1$.

Solve for $x$ if:
$\log_{10}(x - 3) + \log_{10}(x) = 1$

If $\log_2(x) + \log_2(y) = a$ and $\log_2(x) - \log_2(y) = b$, express $x$ and $y$ in terms of $a$ and $b$.