Solve for x
x=\frac{1}{2}=0.5
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7^{8x-2}=49
Use the rules of exponents and logarithms to solve the equation.
\log(7^{8x-2})=\log(49)
Take the logarithm of both sides of the equation.
\left(8x-2\right)\log(7)=\log(49)
The logarithm of a number raised to a power is the power times the logarithm of the number.
8x-2=\frac{\log(49)}{\log(7)}
Divide both sides by \log(7).
8x-2=\log_{7}\left(49\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
8x=2-\left(-2\right)
Add 2 to both sides of the equation.
x=\frac{4}{8}
Divide both sides by 8.
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