Solve for c
c=-\frac{1}{10}=-0.1
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49^{-5c}=7
Use the rules of exponents and logarithms to solve the equation.
\log(49^{-5c})=\log(7)
Take the logarithm of both sides of the equation.
-5c\log(49)=\log(7)
The logarithm of a number raised to a power is the power times the logarithm of the number.
-5c=\frac{\log(7)}{\log(49)}
Divide both sides by \log(49).
-5c=\log_{49}\left(7\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
c=\frac{\frac{1}{2}}{-5}
Divide both sides by -5.
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