Solve 2*3^x-4=5

$$2 \cdot 3 ^ { x - 4 } = 5$$

Solve for x

$$x=\log_{3}\left(\frac{5}{2}\right)+4\approx 4.834043767$$

Steps Using Definition of Logarithm

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

$$2\times 3^{x-4}=5$$

Divide both sides by 2.

$$3^{x-4}=\frac{5}{2}$$

Take the logarithm of both sides of the equation.

$$\log(3^{x-4})=\log(\frac{5}{2})$$

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

$$\left(x-4\right)\log(3)=\log(\frac{5}{2})$$

Divide both sides by \log(3).

$$x-4=\frac{\log(\frac{5}{2})}{\log(3)}$$

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

$$x-4=\log_{3}\left(\frac{5}{2}\right)$$

Add 4 to both sides of the equation.

$$x=\frac{\ln(\frac{5}{2})}{\ln(3)}-\left(-4\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(\frac{5}{2}\right)+4$$

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