Solve 3^x+1=(27*3)^4

$$3 ^ { x + 1 } = ( 27 \cdot 3 ) ^ { 4 }$$

Solve for x

$$x=15$$

Steps Using Definition of Logarithm

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

$$3^{x+1}=43046721$$

Take the logarithm of both sides of the equation.

$$\log(3^{x+1})=\log(43046721)$$

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

$$\left(x+1\right)\log(3)=\log(43046721)$$

Divide both sides by \log(3).

$$x+1=\frac{\log(43046721)}{\log(3)}$$

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

$$x+1=\log_{3}\left(43046721\right)$$

Subtract 1 from both sides of the equation.

$$x=16-1$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+15$$

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