Precalculus Examples

$\log_{14} (3 x + 7) = \log_{14} (2 x - 10)$

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, $b = 14$ , $x = 3 x + 7$ , and $y = \log_{14} (2 x - 10)$ .

$b = 14$

$x = 3 x + 7$

$y = \log_{14} (2 x - 10)$

Step 2

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

$14^{\log_{14} (2 x - 10)} = 3 x + 7$