Solve 3^x/2+3^x=3/2

$$\frac{ { 3 }^{ x } }{ 2 } + { 3 }^{ x } = \frac{ 3 }{ 2 }$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

Multiply both sides of the equation by 2.

$$3^{x}+2\times 3^{x}=3$$

Combine 3^{x} and 2\times 3^{x} to get 3\times 3^{x}.

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

Divide both sides by 3.

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

Divide 3 by 3 to get 1.

$$3^{x}=1$$

Take the logarithm of both sides of the equation.

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

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

$$x\log(3)=\log(1)$$

Divide both sides by \log(3).

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

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

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

Solve for x (complex solution)

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

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