Calculus Examples

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

Step 1

Move all terms not containing $e$ to the right side of the equation.

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Step 1.1

Subtract $\ln (x)$ from both sides of the equation.

$0 = \ln (y^{2} + 1) - \ln (x)$

Step 1.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$0 = \ln (\frac{y^{2} + 1}{x})$

Step 1.3

Split the fraction $\frac{y^{2} + 1}{x}$ into two fractions.

$0 = \ln (\frac{y^{2}}{x} + \frac{1}{x})$

Step 2

Rewrite the equation as $\ln (\frac{y^{2}}{x} + \frac{1}{x}) = 0$ .

$\ln (\frac{y^{2}}{x} + \frac{1}{x}) = 0$