Solve 4000=1500{left(1+0.0625/1right)}^1x

$$4000 = 1500 { \left(1+ \frac{ 0.0625 }{ 1 } \right) }^{ 1x }$$

Solve for x

$$x=\log_{1.0625}\left(\frac{8}{3}\right)\approx 16.178727778$$

Steps Using Definition of Logarithm

Divide both sides by 1500.

$$\frac{4000}{1500}=\left(1+\frac{0.0625}{1}\right)^{1x}$$

Reduce the fraction \frac{4000}{1500} to lowest terms by extracting and canceling out 500.

$$\frac{8}{3}=\left(1+\frac{0.0625}{1}\right)^{1x}$$

Anything divided by one gives itself.

$$\frac{8}{3}=\left(1+0.0625\right)^{1x}$$

Add 1 and 0.0625 to get 1.0625.

$$\frac{8}{3}=1.0625^{1x}$$

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

$$1.0625^{1x}=\frac{8}{3}$$

Subtract \frac{8}{3} from both sides.

$$1.0625^{1x}-\frac{8}{3}=0$$

Reorder the terms.

$$1.0625^{x}-\frac{8}{3}=0$$

Add \frac{8}{3} to both sides of the equation.

$$1.0625^{x}=\frac{8}{3}$$

Take the logarithm of both sides of the equation.

$$\log(1.0625^{x})=\log(\frac{8}{3})$$

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

$$x\log(1.0625)=\log(\frac{8}{3})$$

Divide both sides by \log(1.0625).

$$x=\frac{\log(\frac{8}{3})}{\log(1.0625)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{1.0625}\left(\frac{8}{3}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.0625)}+\log_{1.0625}\left(\frac{8}{3}\right)$$

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