Algebra Examples

$\log_{(x + 4)} (x^{2} + 3 x - 7) = 3$

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, $b = x + 4$ , $x = x^{2} + 3 x - 7$ , and $y = 3$ .

$b = x + 4$

$x = x^{2} + 3 x - 7$

$y = 3$

Step 2

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

${(x + 4)}^{3} = x^{2} + 3 x - 7$