Solve 12=6.13e^0.01x

$$12=6.13 { e }^{ 0.01x }$$

Solve for x

$$x=\ln(\frac{82817974522014550258408423595736849801612281185389443546420186410325491933012122303777028329685801938557337600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{557246631433125119400517539349771820088806169833983801863613344536612309866614486161185938521534819949379274793736444717101467345272655337304971934020498509150962096306624840245699346917464266637558305441567221048547436208322994481064325771961541024804147990965933063390914214001})\approx 67.171189984$$

Steps Using Definition of Logarithm

Divide both sides by 6.13.

$$\frac{12}{6.13}=e^{0.01x}$$

Expand \frac{12}{6.13} by multiplying both numerator and the denominator by 100.

$$\frac{1200}{613}=e^{0.01x}$$

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

$$e^{0.01x}=\frac{1200}{613}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.01x})=\log(\frac{1200}{613})$$

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

$$0.01x\log(e)=\log(\frac{1200}{613})$$

Divide both sides by \log(e).

$$0.01x=\frac{\log(\frac{1200}{613})}{\log(e)}$$

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

$$0.01x=\log_{e}\left(\frac{1200}{613}\right)$$

Multiply both sides by 100.

$$x=\frac{\ln(\frac{1200}{613})}{0.01}$$

Solve for x (complex solution)

$$x=\ln(\frac{82817974522014550258408423595736849801612281185389443546420186410325491933012122303777028329685801938557337600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{557246631433125119400517539349771820088806169833983801863613344536612309866614486161185938521534819949379274793736444717101467345272655337304971934020498509150962096306624840245699346917464266637558305441567221048547436208322994481064325771961541024804147990965933063390914214001})+i\times 200\pi n_{1}$$

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