Solve for x
x=\frac{600\ln(3)-200\ln(5)}{47}\approx 7.17616576
Solve for x (complex solution)
x=-\frac{i\times 400\pi n_{1}}{47}+\frac{600\ln(3)}{47}-\frac{200\ln(5)}{47}
n_{1}\in \mathrm{Z}
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81e^{-0.235x}+15=30
Swap sides so that all variable terms are on the left hand side.
81e^{-0.235x}=15
Subtract 15 from both sides of the equation.
e^{-0.235x}=\frac{5}{27}
Divide both sides by 81.
\log(e^{-0.235x})=\log(\frac{5}{27})
Take the logarithm of both sides of the equation.
-0.235x\log(e)=\log(\frac{5}{27})
The logarithm of a number raised to a power is the power times the logarithm of the number.
-0.235x=\frac{\log(\frac{5}{27})}{\log(e)}
Divide both sides by \log(e).
-0.235x=\log_{e}\left(\frac{5}{27}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=\frac{\ln(\frac{5}{27})}{-0.235}
Divide both sides of the equation by -0.235, which is the same as multiplying both sides by the reciprocal of the fraction.
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