Solve 94=9^3x-1

$$94 = 9 ^ { 3 x } - 1$$

Solve for x

$$x=\frac{\log_{3}\left(95\right)}{6}\approx 0.690852897$$

Steps Using Definition of Logarithm

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

$$9^{3x}-1=94$$

Add 1 to both sides of the equation.

$$9^{3x}=95$$

Take the logarithm of both sides of the equation.

$$\log(9^{3x})=\log(95)$$

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

$$3x\log(9)=\log(95)$$

Divide both sides by \log(9).

$$3x=\frac{\log(95)}{\log(9)}$$

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

$$3x=\log_{9}\left(95\right)$$

Divide both sides by 3.

$$x=\frac{\log_{3}\left(95\right)}{2\times 3}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(3)}+\frac{\log_{3}\left(95\right)}{6}$$

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