Solve 3=(1,06)^x

$$3 = ( 1,06 ) ^ { x }$$

Solve for x

$$x=\log_{1,06}\left(3\right)\approx 18.854176679$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$1,06^{x}=3$$

Take the logarithm of both sides of the equation.

$$\log(1,06^{x})=\log(3)$$

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

$$x\log(1,06)=\log(3)$$

Divide both sides by \log(1,06).

$$x=\frac{\log(3)}{\log(1,06)}$$

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

$$x=\log_{1,06}\left(3\right)$$