Precalculus Examples

$\log (3 \sqrt{x^{2} + 21 x}) = \frac{2}{3}$

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, $b = 10$ , $x = 3 \sqrt{x^{2} + 21 x}$ , and $y = \frac{2}{3}$ .

$b = 10$

$x = 3 \sqrt{x^{2} + 21 x}$

$y = \frac{2}{3}$

Step 2

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

$10^{\frac{2}{3}} = 3 \sqrt{x^{2} + 21 x}$