Precalculus Examples

$\log_{2} (\sqrt{2}) = 4 x$

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, $b = 2$ , $x = \sqrt{2}$ , and $y = 4 x$ .

$b = 2$

$x = \sqrt{2}$

$y = 4 x$

Step 2

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

$2^{4 x} = \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2^{4 x} = \sqrt{2}$

Decimal Form:

$2^{4 x} = 1.41421356 \dots$