Solve (1,03)^x=2

$$( 1,03 ) ^ { x } = 2$$

Solve for x

$$x=\log_{1,03}\left(2\right)\approx 23.44977225$$

Steps Using Definition of Logarithm

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

$$1,03^{x}=2$$

Take the logarithm of both sides of the equation.

$$\log(1,03^{x})=\log(2)$$

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

$$x\log(1,03)=\log(2)$$

Divide both sides by \log(1,03).

$$x=\frac{\log(2)}{\log(1,03)}$$

By the change-of-base formula log(a)/log(b)=log(b,a).

$$x=\log_{1,03}\left(2\right)$$