Solve 3^7+3^7+3^7=3^x

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

Solve for x

$$x=8$$

Steps Using Definition of Logarithm

Calculate 3 to the power of 7 and get 2187.

$$2187+3^{7}+3^{7}=3^{x}$$

Calculate 3 to the power of 7 and get 2187.

$$2187+2187+3^{7}=3^{x}$$

Add 2187 and 2187 to get 4374.

$$4374+3^{7}=3^{x}$$

Calculate 3 to the power of 7 and get 2187.

$$4374+2187=3^{x}$$

Add 4374 and 2187 to get 6561.

$$6561=3^{x}$$

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

$$3^{x}=6561$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(6561)$$

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

$$x\log(3)=\log(6561)$$

Divide both sides by \log(3).

$$x=\frac{\log(6561)}{\log(3)}$$

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

$$x=\log_{3}\left(6561\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+8$$

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