Solve 9261=8000[1+5/100]^T

$$9261 = 8000 [ \frac { 1 + 5 } { 100 } ] ^ { T }$$

Solve for T

$$T=3\log_{\frac{3}{50}}\left(\frac{21}{20}\right)\approx -0.052025995$$

Steps Using Definition of Logarithm

Divide both sides by 8000.

$$\frac{9261}{8000}=\left(\frac{1+5}{100}\right)^{T}$$

Add 1 and 5 to get 6.

$$\frac{9261}{8000}=\left(\frac{6}{100}\right)^{T}$$

Reduce the fraction \frac{6}{100} to lowest terms by extracting and canceling out 2.

$$\frac{9261}{8000}=\left(\frac{3}{50}\right)^{T}$$

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

$$\left(\frac{3}{50}\right)^{T}=\frac{9261}{8000}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{3}{50}\right)^{T})=\log(\frac{9261}{8000})$$

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

$$T\log(\frac{3}{50})=\log(\frac{9261}{8000})$$

Divide both sides by \log(\frac{3}{50}).

$$T=\frac{\log(\frac{9261}{8000})}{\log(\frac{3}{50})}$$

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

$$T=\log_{\frac{3}{50}}\left(\frac{9261}{8000}\right)$$