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Solve for x
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Solve for x (complex solution)
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\frac{20000}{2000}=e^{0.195\times 20x}
Divide both sides by 2000.
10=e^{0.195\times 20x}
Divide 20000 by 2000 to get 10.
10=e^{3.9x}
Multiply 0.195 and 20 to get 3.9.
e^{3.9x}=10
Swap sides so that all variable terms are on the left hand side.
\log(e^{3.9x})=\log(10)
Take the logarithm of both sides of the equation.
3.9x\log(e)=\log(10)
The logarithm of a number raised to a power is the power times the logarithm of the number.
3.9x=\frac{\log(10)}{\log(e)}
Divide both sides by \log(e).
3.9x=\log_{e}\left(10\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\ln(10)}{3.9}
Divide both sides of the equation by 3.9, which is the same as multiplying both sides by the reciprocal of the fraction.