Solve 3^3x+1-1=7+5

$$3 ^ { 3 x + 1 } - 1 = 7 + 5$$

Solve for x

$$x=\frac{\log_{3}\left(13\right)-1}{3}\approx 0.44490584$$

Steps Using Definition of Logarithm

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

$$3^{3x+1}-1=12$$

Add 1 to both sides of the equation.

$$3^{3x+1}=13$$

Take the logarithm of both sides of the equation.

$$\log(3^{3x+1})=\log(13)$$

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

$$\left(3x+1\right)\log(3)=\log(13)$$

Divide both sides by \log(3).

$$3x+1=\frac{\log(13)}{\log(3)}$$

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

$$3x+1=\log_{3}\left(13\right)$$

Subtract 1 from both sides of the equation.

$$3x=\log_{3}\left(13\right)-1$$

Divide both sides by 3.

$$x=\frac{\log_{3}\left(13\right)-1}{3}$$