Solve 100=(6)2.718^12.72x

$$100 = ( 6 ) 2.718 ^ { 12.72 x }$$

Solve for x

$$x=-\frac{25\ln(0.06)}{318\ln(1359)-318\ln(500)}\approx 0.221203023$$

Steps Using Definition of Logarithm

Divide both sides by 6.

$$\frac{100}{6}=2.718^{12.72x}$$

Reduce the fraction \frac{100}{6} to lowest terms by extracting and canceling out 2.

$$\frac{50}{3}=2.718^{12.72x}$$

Swap sides so that all variable terms are on the left hand side.

$$2.718^{12.72x}=\frac{50}{3}$$

Take the logarithm of both sides of the equation.

$$\log(2.718^{12.72x})=\log(\frac{50}{3})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$12.72x\log(2.718)=\log(\frac{50}{3})$$

Divide both sides by \log(2.718).

$$12.72x=\frac{\log(\frac{50}{3})}{\log(2.718)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$12.72x=\log_{2.718}\left(\frac{50}{3}\right)$$

Divide both sides of the equation by 12.72, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(\frac{50}{3})}{12.72\ln(\frac{1359}{500})}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\times 25\pi n_{1}}{318\ln(1359)-318\ln(500)}-\frac{25\ln(0.06)}{318\ln(1359)-318\ln(500)}$$

$$n_{1}\in \mathrm{Z}$$