Solve 10^1-x=30

$$10 ^ { 1 - x } = 30$$

Solve for x

$$x=-\log(3)\approx -0.477121255$$

Steps Using Definition of Logarithm

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

$$10^{-x+1}=30$$

Take the logarithm of both sides of the equation.

$$\log(10^{-x+1})=\log(30)$$

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

$$\left(-x+1\right)\log(10)=\log(30)$$

Subtract 1 from both sides of the equation.

$$-x=\log(30)-1$$

Divide both sides by -1.

$$x=\frac{\log(30)-1}{-1}$$

Solve for x (complex solution)

$$x=-2\pi n_{1}i\log(e)-\log(3)$$

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