Calculus Examples

{log}_{27} (x - 1) = {log}_{81} (2 x + 3)

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

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

$b^{y} = x$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$