Trigonometry Examples

$2 \log_{5} (x) = 3 \log_{5} (4)$

Step 1

Simplify $2 \log_{5} (x)$ by moving $2$ inside the logarithm.

$\log_{5} (x^{2}) = 3 \log_{5} (4)$

Step 2

Simplify $3 \log_{5} (4)$ .

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Step 2.1

Simplify $3 \log_{5} (4)$ by moving $3$ inside the logarithm.

$\log_{5} (x^{2}) = \log_{5} (4^{3})$

Step 2.2

Raise $4$ to the power of $3$ .

$\log_{5} (x^{2}) = \log_{5} (64)$

Step 3

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

$x = 8$

Step 4