Precalculus Examples

$2 {(3)}^{2 x} = 5$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$2 \cdot 3^{2 x} = 5$

Step 1.2

Divide each term in $2 \cdot 3^{2 x} = 5$ by $2$ .

$\frac{2 \cdot 3^{2 x}}{2} = \frac{5}{2}$

Step 1.3

Reduce by cancelling the common factors.

$3^{2 x} = \frac{5}{2}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(3)$ of the right side $(\frac{5}{2})$ equals the exponent $(2 x)$ .

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