Finite Math Examples

$\ln (x) = 7 y - 2$

Step 1

Rewrite the equation as $7 y - 2 = \ln (x)$ .

$7 y - 2 = \ln (x)$

Step 2

Add $2$ to both sides of the equation.

$7 y = \ln (x) + 2$

Step 3

Divide each term in $7 y = \ln (x) + 2$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 y = \ln (x) + 2$ by $7$ .

$\frac{7 y}{7} = \frac{\ln (x)}{7} + \frac{2}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{\ln (x)}{7} + \frac{2}{7}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\ln (x)}{7} + \frac{2}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite $\frac{\ln (x)}{7}$ as $\frac{1}{7} \ln (x)$ .

$y = \frac{1}{7} \ln (x) + \frac{2}{7}$

Step 3.3.1.2

Simplify $\frac{1}{7} \ln (x)$ by moving $\frac{1}{7}$ inside the logarithm.

$y = \ln (x^{\frac{1}{7}}) + \frac{2}{7}$