Precalculus Examples

$2 a^{\frac{t}{3}} = 5$

Step 1

Simplify.

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Step 1.1

Divide each term in $2 a^{\frac{t}{3}} = 5$ by $2$ .

$\frac{2 a^{\frac{t}{3}}}{2} = \frac{5}{2}$

Step 1.2

Reduce by cancelling the common factors.

$a^{\frac{t}{3}} = \frac{5}{2}$

Step 2

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

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