Finite Math Examples

$y = \log_{0.75} ((x - 2) + 1)$

Step 1

Rewrite the equation as $\log_{0.75} (x - 2 + 1) = y$ .

$\log_{0.75} (x - 2 + 1) = y$

Step 2

Rewrite $\log_{0.75} (x - 2 + 1) = y$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

${0.75}^{y} = x - 2 + 1$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x - 2 + 1 = {0.75}^{y}$ .

$x - 2 + 1 = {0.75}^{y}$

Step 3.2

Add $- 2$ and $1$ .

$x - 1 = {0.75}^{y}$

Step 3.3

Add $1$ to both sides of the equation.

$x = {0.75}^{y} + 1$