Solve 2*10^2-x=5

$$2 \cdot 10 ^ { 2 - x } = 5$$

Solve for x

$$x=\log_{10}\left(40\right)\approx 1.602059991$$

Steps Using Definition of Logarithm

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

$$2\times 10^{-x+2}=5$$

Divide both sides by 2.

$$10^{-x+2}=\frac{5}{2}$$

Take the logarithm of both sides of the equation.

$$\log(10^{-x+2})=\log(\frac{5}{2})$$

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

$$\left(-x+2\right)\log(10)=\log(\frac{5}{2})$$

Subtract 2 from both sides of the equation.

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

Divide both sides by -1.

$$x=\frac{\log(\frac{5}{2})-2}{-1}$$

Solve for x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(10)}+\log_{10}\left(40\right)$$

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