Algebra Examples

$\log_{4} (x) = \log_{4} (15) - \log_{4} (3)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $\log_{4} (15) - \log_{4} (3)$ .

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Step 1.1.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (x) = \log_{4} (\frac{15}{3})$

Step 1.1.2

Divide $15$ by $3$ .

$\log_{4} (x) = \log_{4} (5)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x = 5$