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Solve for x
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Solve for x (complex solution)
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\frac{100000000}{67}=1.026^{x}
Divide both sides by 67.
1.026^{x}=\frac{100000000}{67}
Swap sides so that all variable terms are on the left hand side.
\log(1.026^{x})=\log(\frac{100000000}{67})
Take the logarithm of both sides of the equation.
x\log(1.026)=\log(\frac{100000000}{67})
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(\frac{100000000}{67})}{\log(1.026)}
Divide both sides by \log(1.026).
x=\log_{1.026}\left(\frac{100000000}{67}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).