Algebra Examples

$3 \log_{4} (x) = \log_{4} (32) + \log_{4} (2)$

Step 1

Simplify $3 \log_{4} (x)$ by moving $3$ inside the logarithm.

$\log_{4} (x^{3}) = \log_{4} (32) + \log_{4} (2)$

Step 2

Simplify $\log_{4} (32) + \log_{4} (2)$ .

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Step 2.1

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

$\log_{4} (x^{3}) = \log_{4} (32 \cdot 2)$

Step 2.2

Multiply $32$ by $2$ .

$\log_{4} (x^{3}) = \log_{4} (64)$

Step 2.3

Logarithm base $4$ of $64$ is $3$ .

$\log_{4} (x^{3}) = 3$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 4$

Step 4