Solve 9600=4800(1+5*5/100)^x

$$9600 = 4800 ( 1 + 5 \cdot 5 / 100 ) ^ { x }$$

Solve for x

$$x=\log_{\frac{5}{4}}\left(2\right)\approx 3.10628372$$

Steps Using Definition of Logarithm

Divide both sides by 4800.

$$\frac{9600}{4800}=\left(1+5\times \frac{5}{100}\right)^{x}$$

Divide 9600 by 4800 to get 2.

$$2=\left(1+5\times \frac{5}{100}\right)^{x}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$2=\left(1+5\times \frac{1}{20}\right)^{x}$$

Multiply 5 and \frac{1}{20} to get \frac{1}{4}.

$$2=\left(1+\frac{1}{4}\right)^{x}$$

Add 1 and \frac{1}{4} to get \frac{5}{4}.

$$2=\left(\frac{5}{4}\right)^{x}$$

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

$$\left(\frac{5}{4}\right)^{x}=2$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{5}{4}\right)^{x})=\log(2)$$

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

$$x\log(\frac{5}{4})=\log(2)$$

Divide both sides by \log(\frac{5}{4}).

$$x=\frac{\log(2)}{\log(\frac{5}{4})}$$

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

$$x=\log_{\frac{5}{4}}\left(2\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{5}{4})}+\log_{\frac{5}{4}}\left(2\right)$$

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