Algebra Examples

$\log_{2 x} (x^{2} - 5 x + 17) = 3 x$

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, $b = 2 x$ , $x = x^{2} - 5 x + 17$ , and $y = 3 x$ .

$b = 2 x$

$x = x^{2} - 5 x + 17$

$y = 3 x$

Step 2

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

$2 x^{3 x} = x^{2} - 5 x + 17$