Precalculus Examples

$\log_{3} (\sqrt{27}) = x$

Step 1

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 3$ , $x = \sqrt{27}$ , and $y = x$ .

$b = 3$

$x = \sqrt{27}$

$y = x$

Step 2

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$3^{x} = \sqrt{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3^{x} = \sqrt{27}$

Decimal Form:

$3^{x} = 5.19615242 \dots$