Finite Math Examples

$y = 2^{x} - 12$

Step 1

Rewrite the equation as $2^{x} - 12 = y$ .

$2^{x} - 12 = y$

Step 2

Add $12$ to both sides of the equation.

$2^{x} = y + 12$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{x}) = \ln (y + 12)$

Step 4

Expand $\ln (2^{x})$ by moving $x$ outside the logarithm.

$x \ln (2) = \ln (y + 12)$

Step 5

Divide each term in $x \ln (2) = \ln (y + 12)$ by $\ln (2)$ and simplify.

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Step 5.1

Divide each term in $x \ln (2) = \ln (y + 12)$ by $\ln (2)$ .

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (y + 12)}{\ln (2)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (2)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (y + 12)}{\ln (2)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (y + 12)}{\ln (2)}$