Algebra Examples

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

Step 1

Simplify.

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Step 1.1

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

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

Step 1.2

Divide $30$ by $2$ .

$15$

Step 1.3

Reduce by cancelling the common factors.

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

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(3)$ of the right side $(15)$ equals the exponent $(\frac{2 x}{7})$ .

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