Calculus Examples

$\log_{27} (x - 1) = \log_{81} (2 x + 3)$

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, $b = 27$ , $x = x - 1$ , and $y = \log_{81} (2 x + 3)$ .

$b = 27$

$x = x - 1$

$y = \log_{81} (2 x + 3)$

Step 2

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

$27^{\log_{81} (2 x + 3)} = x - 1$