Solve 3^5x+8-243=0

$$3 ^ { 5 x + 8 } - 243 = 0$$

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Steps Using Definition of Logarithm

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

$$3^{5x+8}-243=0$$

Add 243 to both sides of the equation.

$$3^{5x+8}=243$$

Take the logarithm of both sides of the equation.

$$\log(3^{5x+8})=\log(243)$$

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

$$\left(5x+8\right)\log(3)=\log(243)$$

Divide both sides by \log(3).

$$5x+8=\frac{\log(243)}{\log(3)}$$

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

$$5x+8=\log_{3}\left(243\right)$$

Subtract 8 from both sides of the equation.

$$5x=5-8$$

Divide both sides by 5.

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

Solve for x (complex solution)

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

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