Algebra Examples

$\log_{x} (4) + \log_{x} (2) = 1$

Step 1

Simplify the left side.

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Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{x} (4 \cdot 2) = 1$

Step 1.2

Multiply $4$ by $2$ .

$\log_{x} (8) = 1$

Step 2

Rewrite $\log_{x} (8) = 1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$x^{1} = 8$

Step 3

Simplify.

$x = 8$