Algebra Examples

$\log_{a} (x) = 2 \log_{a} (3) + \log_{a} (5)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $2 \log_{a} (3) + \log_{a} (5)$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Simplify $2 \log_{a} (3)$ by moving $2$ inside the logarithm.

$\log_{a} (x) = \log_{a} (3^{2}) + \log_{a} (5)$

Step 1.1.1.2

Raise $3$ to the power of $2$ .

$\log_{a} (x) = \log_{a} (9) + \log_{a} (5)$

Step 1.1.2

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

$\log_{a} (x) = \log_{a} (9 \cdot 5)$

Step 1.1.3

Multiply $9$ by $5$ .

$\log_{a} (x) = \log_{a} (45)$

Step 2

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

$x = 45$