Solve 9600=1500*2^x

$$9600=1500 \times { 2 }^{ x }$$

Solve for x

$$x=-\log_{2}\left(5\right)+5\approx 2.678071905$$

Steps Using Definition of Logarithm

Divide both sides by 1500.

$$\frac{9600}{1500}=2^{x}$$

Reduce the fraction \frac{9600}{1500} to lowest terms by extracting and canceling out 300.

$$\frac{32}{5}=2^{x}$$

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

$$2^{x}=\frac{32}{5}$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(\frac{32}{5})$$

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

$$x\log(2)=\log(\frac{32}{5})$$

Divide both sides by \log(2).

$$x=\frac{\log(\frac{32}{5})}{\log(2)}$$

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

$$x=\log_{2}\left(\frac{32}{5}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}-\log_{2}\left(5\right)+5$$

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