Solve for t
t=\log_{85}\left(\frac{2}{3}\right)\approx -0.091266472
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85^{t}=\frac{2}{3}
Use the rules of exponents and logarithms to solve the equation.
\log(85^{t})=\log(\frac{2}{3})
Take the logarithm of both sides of the equation.
t\log(85)=\log(\frac{2}{3})
The logarithm of a number raised to a power is the power times the logarithm of the number.
t=\frac{\log(\frac{2}{3})}{\log(85)}
Divide both sides by \log(85).
t=\log_{85}\left(\frac{2}{3}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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