Solve 10^3x-4=13

$$10 ^ { 3 x - 4 } = 13$$

Solve for x

$$x = \frac{\log_{10} {(13)} + 4}{3} \approx 1.704647784$$

Steps Using Definition of Logarithm

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

$$10^{3x-4}=13$$

Take the logarithm of both sides of the equation.

$$\log(10^{3x-4})=\log(13)$$

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

$$\left(3x-4\right)\log(10)=\log(13)$$

Add 4 to both sides of the equation.

$$3x=\log(13)-\left(-4\right)$$

Divide both sides by 3.

$$x=\frac{\log(13)+4}{3}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i\log(e)}{3}+\frac{\log(13)+4}{3}$$

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