Solve 500=2(1,07)^t

$$500 = 2 ( 1,07 ) ^ { t }$$

Solve for t

$$t=\log_{1,07}\left(250\right)\approx 81.607614731$$

Steps Using Definition of Logarithm

Divide both sides by 2.

$$\frac{500}{2}=1,07^{t}$$

Divide 500 by 2 to get 250.

$$250=1,07^{t}$$

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

$$1,07^{t}=250$$

Take the logarithm of both sides of the equation.

$$\log(1,07^{t})=\log(250)$$

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

$$t\log(1,07)=\log(250)$$

Divide both sides by \log(1,07).

$$t=\frac{\log(250)}{\log(1,07)}$$

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

$$t=\log_{1,07}\left(250\right)$$