Solve 4*3^x+3^x=15

$$4 \cdot 3 ^ { x } + 3 ^ { x } = 15$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

Combine 4\times 3^{x} and 3^{x} to get 5\times 3^{x}.

$$5\times 3^{x}=15$$

Divide both sides by 5.

$$3^{x}=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$3^{x}=3$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(3).

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

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

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

Solve for x (complex solution)

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

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