Precalculus Examples

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

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, $b = a$ , $x = \sqrt{3}$ , and $y = x$ .

$b = a$

$x = \sqrt{3}$

$y = x$

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a^{x} = 1.73205080 \dots$