Solve for x 2*3^((2x)/7)=30

$2 \cdot 3^{\frac{2 x}{7}} = 30$

Step 1

Divide each term in $(2 \cdot 3^{\frac{2 x}{7}}) = 30$ by $2$ and simplify.

Divide each term in $(2 \cdot 3^{\frac{2 x}{7}}) = 30$ by $2$ .

$\frac{(2 \cdot 3^{\frac{2 x}{7}})}{2} = \frac{30}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 3^{\frac{2 x}{7}}}{2} = \frac{30}{2}$

Divide $3^{\frac{2 x}{7}}$ by $1$ .

$3^{\frac{2 x}{7}} = \frac{30}{2}$

Simplify the right side.

Divide $30$ by $2$ .

$3^{\frac{2 x}{7}} = 15$

Step 2

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

$\ln (3^{\frac{2 x}{7}}) = \ln (15)$

Step 3

Expand the left side.

Expand $\ln (3^{\frac{2 x}{7}})$ by moving $\frac{2 x}{7}$ outside the logarithm.

$\frac{2 x}{7} \ln (3) = \ln (15)$

Combine $\frac{2 x}{7}$ and $\ln (3)$ .

$\frac{2 x \ln (3)}{7} = \ln (15)$

Step 4

Multiply both sides of the equation by $\frac{1}{2 \frac{\ln (3)}{7}}$ .

$\frac{1}{2 \frac{\ln (3)}{7}} \cdot \frac{2 x \ln (3)}{7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{1}{2 \frac{\ln (3)}{7}} \cdot \frac{2 x \ln (3)}{7}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $2 \frac{\ln (3)}{7}$ .

$\frac{1}{2 (\frac{\ln (3)}{7})} \cdot \frac{2 x \ln (3)}{7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Factor $2$ out of $2 x \ln (3)$ .

$\frac{1}{2 (\frac{\ln (3)}{7})} \cdot \frac{2 (x \ln (3))}{7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Cancel the common factor.

$\frac{1}{2 \frac{\ln (3)}{7}} \cdot \frac{2 (x \ln (3))}{7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Rewrite the expression.

$\frac{1}{\frac{\ln (3)}{7}} \cdot \frac{x \ln (3)}{7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Multiply $\frac{1}{\frac{\ln (3)}{7}}$ by $\frac{x \ln (3)}{7}$ .

$\frac{x \ln (3)}{\frac{\ln (3)}{7} \cdot 7} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Combine $\frac{\ln (3)}{7}$ and $7$ .

$\frac{x \ln (3)}{\frac{\ln (3) \cdot 7}{7}} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{x \ln (3)}{\frac{\ln (3) \cdot 7}{7}} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Divide $\ln (3)$ by $1$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Divide $x$ by $1$ .

$x = \frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$

Simplify the right side.

Simplify $\frac{1}{2 \frac{\ln (3)}{7}} \ln (15)$ .

Combine $2$ and $\frac{\ln (3)}{7}$ .

$x = \frac{1}{\frac{2 \ln (3)}{7}} \ln (15)$

Multiply the numerator by the reciprocal of the denominator.

$x = 1 \frac{7}{2 \ln (3)} \ln (15)$

Multiply $\frac{7}{2 \ln (3)}$ by $1$ .

$x = \frac{7}{2 \ln (3)} \ln (15)$

Combine $\frac{7}{2 \ln (3)}$ and $\ln (15)$ .

$x = \frac{7 \ln (15)}{2 \ln (3)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \ln (15)}{2 \ln (3)}$

Decimal Form:

$x = 8.62740732 \dots$

Solve for x 2*3^((2x)/7)=30

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