Trigonometry Examples

$y = 3 \ln (x)$

Step 1

Rewrite the equation as $3 \ln (x) = y$ .

$3 \ln (x) = y$

Step 2

Divide each term in $3 \ln (x) = y$ by $3$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $3 \ln (x) = y$ by $3$ .

$\frac{3 \ln (x)}{3} = \frac{y}{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{3 \ln (x)}{3} = \frac{y}{3}$

Step 2.2.1.2

Divide $\ln (x)$ by $1$ .

$\ln (x) = \frac{y}{3}$

Step 3

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x)} = e^{\frac{y}{3}}$

Step 4

Rewrite $\ln (x) = \frac{y}{3}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{\frac{y}{3}} = x$

Step 5

Rewrite the equation as $x = e^{\frac{y}{3}}$ .

$x = e^{\frac{y}{3}}$