Solve (3/5)^6(3/5)^6=(3/5)^3x

$$( \frac { 3 } { 5 } ) ^ { 6 } ( \frac { 3 } { 5 } ) ^ { 6 } = ( \frac { 3 } { 5 } ) ^ { 3 x }$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\left(\frac{3}{5}\right)^{12}=\left(\frac{3}{5}\right)^{3x}$$

Calculate \frac{3}{5} to the power of 12 and get \frac{531441}{244140625}.

$$\frac{531441}{244140625}=\left(\frac{3}{5}\right)^{3x}$$

Swap sides so that all variable terms are on the left hand side.

$$\left(\frac{3}{5}\right)^{3x}=\frac{531441}{244140625}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{3}{5}\right)^{3x})=\log(\frac{531441}{244140625})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$3x\log(\frac{3}{5})=\log(\frac{531441}{244140625})$$

Divide both sides by \log(\frac{3}{5}).

$$3x=\frac{\log(\frac{531441}{244140625})}{\log(\frac{3}{5})}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$3x=\log_{\frac{3}{5}}\left(\frac{531441}{244140625}\right)$$

Divide both sides by 3.

$$x=\frac{12}{3}$$