Precalculus Examples

$\log_{0.6} ({1.5}^{x}) = - x$

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, $b = 0.6$ , $x = {1.5}^{x}$ , and $y = - x$ .

$b = 0.6$

$x = {1.5}^{x}$

$y = - x$

Step 2

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

${0.6}^{- x} = {1.5}^{x}$