Trigonometry Examples

$19^{a} = b$

Step 1

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

$\ln (19^{a}) = \ln (b)$

Step 2

Expand $\ln (19^{a})$ by moving $a$ outside the logarithm.

$a \ln (19) = \ln (b)$

Step 3

Divide each term in $a \ln (19) = \ln (b)$ by $\ln (19)$ and simplify.

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Step 3.1

Divide each term in $a \ln (19) = \ln (b)$ by $\ln (19)$ .

$\frac{a \ln (19)}{\ln (19)} = \frac{\ln (b)}{\ln (19)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\ln (19)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a \ln (19)}{\ln (19)} = \frac{\ln (b)}{\ln (19)}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{\ln (b)}{\ln (19)}$