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125\times 0.858^{t}+65=70
Use the rules of exponents and logarithms to solve the equation.
125\times 0.858^{t}=5
Subtract 65 from both sides of the equation.
0.858^{t}=\frac{1}{25}
Divide both sides by 125.
\log(0.858^{t})=\log(\frac{1}{25})
Take the logarithm of both sides of the equation.
t\log(0.858)=\log(\frac{1}{25})
The logarithm of a number raised to a power is the power times the logarithm of the number.
t=\frac{\log(\frac{1}{25})}{\log(0.858)}
Divide both sides by \log(0.858).
t=\log_{0.858}\left(\frac{1}{25}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).