Solve 27*3^5x=9

$$27 \cdot 3 ^ { 5 x } = 9$$

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$27\times 3^{5x}=9$$

Divide both sides by 27.

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(3).

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

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

$$5x=\log_{3}\left(\frac{1}{3}\right)$$

Divide both sides by 5.

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

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}-\frac{1}{5}$$

$$n_{1}\in \mathrm{Z}$$