Trigonometry Examples

$\ln (4 y) = \ln (9 + \ln (12))$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$4 y = 9 + \ln (12)$

Step 2

Divide each term in $4 y = 9 + \ln (12)$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y = 9 + \ln (12)$ by $4$ .

$\frac{4 y}{4} = \frac{9}{4} + \frac{\ln (12)}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{9}{4} + \frac{\ln (12)}{4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{4} + \frac{\ln (12)}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Rewrite $\frac{\ln (12)}{4}$ as $\frac{1}{4} \ln (12)$ .

$y = \frac{9}{4} + \frac{1}{4} \ln (12)$

Step 2.3.1.2

Simplify $\frac{1}{4} \ln (12)$ by moving $\frac{1}{4}$ inside the logarithm.

$y = \frac{9}{4} + \ln (12^{\frac{1}{4}})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{9}{4} + \ln (12^{\frac{1}{4}})$

Decimal Form:

$y = 2.87122666 \dots$