Finite Math Examples

$\log_{x} (9) = \log_{x} (\frac{1}{3})$

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, $b = x$ , $x = 9$ , and $y = \log_{x} (\frac{1}{3})$ .

$b = x$

$x = 9$

$y = \log_{x} (\frac{1}{3})$

Step 2

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

$x^{\log_{x} (\frac{1}{3})} = 9$