NationalHardAlgebra10–12

Solving a Logarithmic Equation

Resolver uma Equação Logarítmica

Solve $\log_{2}(x) + \log_{2}(x - 2) = 3$ in $\mathbb{R}$ .

A sum of logarithms with the same base can be rewritten as a single logarithm. Before you solve anything, work out which values of $x$ the original equation even allows — that condition is what settles the answer at the end.

Solution

Step 1 of 6

1.Domain: $x > 0$ and $x - 2 > 0$ , so $x > 2$ .