Solve for t
t=\log_{\frac{23}{20}}\left(6\right)\approx 12.820081338
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\left(\frac{23}{20}\right)^{t}=6
Swap sides so that all variable terms are on the left hand side.
\log(\left(\frac{23}{20}\right)^{t})=\log(6)
Take the logarithm of both sides of the equation.
t\log(\frac{23}{20})=\log(6)
The logarithm of a number raised to a power is the power times the logarithm of the number.
t=\frac{\log(6)}{\log(\frac{23}{20})}
Divide both sides by \log(\frac{23}{20}).
t=\log_{\frac{23}{20}}\left(6\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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