Solve for x 3*3^(x/5)=1

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

Step 1

Multiply $3$ by $3^{\frac{x}{5}}$ .

Raise $3$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2

Divide each term in $3^{1 + \frac{x}{5}} = 1$ by $3$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $3^{1 + \frac{x}{5}}$ and $3$ .

Factor $3$ out of $3^{1 + \frac{x}{5}}$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

Raise $3$ to the power of $1$ .

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

Step 4

Move $3^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 5

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

$\frac{x}{5} = - 1$

Step 6

Solve for $x$ .

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot - 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot - 1$

Rewrite the expression.

$x = 5 \cdot - 1$

Simplify the right side.

Multiply $5$ by $- 1$ .

$x = - 5$

Solve for x 3*3^(x/5)=1

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