Solve 9^x+10+3=8

$${ 9 }^{ x+10 } +3=8$$

Solve for x

$$x=\frac{\log_{3}\left(5\right)-20}{2}\approx -9.26751324$$

Steps Using Definition of Logarithm

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

$$9^{x+10}+3=8$$

Subtract 3 from both sides of the equation.

$$9^{x+10}=5$$

Take the logarithm of both sides of the equation.

$$\log(9^{x+10})=\log(5)$$

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

$$\left(x+10\right)\log(9)=\log(5)$$

Divide both sides by \log(9).

$$x+10=\frac{\log(5)}{\log(9)}$$

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

$$x+10=\log_{9}\left(5\right)$$

Subtract 10 from both sides of the equation.

$$x=\frac{\log_{3}\left(5\right)}{2}-10$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+\frac{\log_{3}\left(5\right)}{2}-10$$

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