Solve 5(3)^x-4=50

$$5 ( 3 ) ^ { x - 4 } = 50$$

Solve for x

$$x=\log_{3}\left(10\right)+4\approx 6.095903274$$

Steps Using Definition of Logarithm

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

$$5\times 3^{x-4}=50$$

Divide both sides by 5.

$$3^{x-4}=10$$

Take the logarithm of both sides of the equation.

$$\log(3^{x-4})=\log(10)$$

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

$$\left(x-4\right)\log(3)=\log(10)$$

Divide both sides by \log(3).

$$x-4=\frac{\log(10)}{\log(3)}$$

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

$$x-4=\log_{3}\left(10\right)$$

Add 4 to both sides of the equation.

$$x=\log_{3}\left(10\right)-\left(-4\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(10\right)+4$$

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