Solve 3^7x+6=9?

$$3 ^ { 7 x + 6 } = 9 ?$$

Solve for x

$$x=-\frac{4}{7}\approx -0.571428571$$

Steps Using Definition of Logarithm

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

$$3^{7x+6}=9$$

Take the logarithm of both sides of the equation.

$$\log(3^{7x+6})=\log(9)$$

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

$$\left(7x+6\right)\log(3)=\log(9)$$

Divide both sides by \log(3).

$$7x+6=\frac{\log(9)}{\log(3)}$$

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

$$7x+6=\log_{3}\left(9\right)$$

Subtract 6 from both sides of the equation.

$$7x=2-6$$

Divide both sides by 7.

$$x=-\frac{4}{7}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{7\ln(3)}-\frac{4}{7}$$

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