Solve for x 36(1/3)^(x/5)=4

$36 {(\frac{1}{3})}^{\frac{x}{5}} = 4$

Divide each term by $36$ and simplify.

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Divide each term in $36 {(\frac{1}{3})}^{\frac{x}{5}} = 4$ by $36$ .

$\frac{36 {(\frac{1}{3})}^{\frac{x}{5}}}{36} = \frac{4}{36}$

Simplify $\frac{36 {(\frac{1}{3})}^{\frac{x}{5}}}{36}$ .

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Cancel the common factor of $36$ .

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Cancel the common factor.

$\frac{36 {(\frac{1}{3})}^{\frac{x}{5}}}{36} = \frac{4}{36}$

Divide ${(\frac{1}{3})}^{\frac{x}{5}}$ by $1$ .

${(\frac{1}{3})}^{\frac{x}{5}} = \frac{4}{36}$

Simplify the expression.

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Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{\frac{x}{5}}}{3^{\frac{x}{5}}} = \frac{4}{36}$

One to any power is one.

$\frac{1}{3^{\frac{x}{5}}} = \frac{4}{36}$

Cancel the common factor of $4$ and $36$ .

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Factor $4$ out of $4$ .

$\frac{1}{3^{\frac{x}{5}}} = \frac{4 (1)}{36}$

Cancel the common factors.

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Factor $4$ out of $36$ .

$\frac{1}{3^{\frac{x}{5}}} = \frac{4 \cdot 1}{4 \cdot 9}$

Cancel the common factor.

$\frac{1}{3^{\frac{x}{5}}} = \frac{4 \cdot 1}{4 \cdot 9}$

Rewrite the expression.

$\frac{1}{3^{\frac{x}{5}}} = \frac{1}{9}$

Solve for $x$ .

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Multiply each term by $3^{\frac{x}{5}}$ and simplify.

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Multiply each term in $\frac{1}{3^{\frac{x}{5}}} = \frac{1}{9}$ by $3^{\frac{x}{5}}$ .

$\frac{1}{3^{\frac{x}{5}}} \cdot 3^{\frac{x}{5}} = \frac{1}{9} \cdot 3^{\frac{x}{5}}$

Cancel the common factor of $3^{\frac{x}{5}}$ .

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Cancel the common factor.

$\frac{1}{3^{\frac{x}{5}}} \cdot 3^{\frac{x}{5}} = \frac{1}{9} \cdot 3^{\frac{x}{5}}$

Rewrite the expression.

$1 = \frac{1}{9} \cdot 3^{\frac{x}{5}}$

Combine $\frac{1}{9}$ and $3^{\frac{x}{5}}$ .

$1 = \frac{3^{\frac{x}{5}}}{9}$

Rewrite the equation as $\frac{3^{\frac{x}{5}}}{9} = 1$ .

$\frac{3^{\frac{x}{5}}}{9} = 1$

Multiply both sides of the equation by $9$ .

$9 \cdot \frac{3^{\frac{x}{5}}}{9} = 9 \cdot 1$

Simplify both sides of the equation.

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Cancel the common factor of $9$ .

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Cancel the common factor.

$9 \cdot \frac{3^{\frac{x}{5}}}{9} = 9 \cdot 1$

Rewrite the expression.

$3^{\frac{x}{5}} = 9 \cdot 1$

Multiply $9$ by $1$ .

$3^{\frac{x}{5}} = 9$

Create equivalent expressions in the equation that all have equal bases.

$3^{\frac{x}{5}} = 3^{2}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$\frac{x}{5} = 2$

Solve for $x$ .

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Multiply both sides of the equation by $5$ .

$5 \cdot \frac{x}{5} = 5 \cdot 2$

Simplify both sides of the equation.

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Cancel the common factor of $5$ .

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Cancel the common factor.

$5 \cdot \frac{x}{5} = 5 \cdot 2$

Rewrite the expression.

$x = 5 \cdot 2$

Multiply $5$ by $2$ .

$x = 10$

Solve for x 36(1/3)^(x/5)=4

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