Solve 10=5.54e^0.01x

$$10 = 5.54 e ^ { 0.01 x }$$

Solve for x

$$x=\ln(\frac{788860905221011805411728565282786229673206435109023004770278930664062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{17700148354958811197049631856692489668047119251071967293590862465287624612244991691538040557195928283779646387164477206241990791955440628457965897872597303746777718964761302600178359096074101138450296604892200209625205282428068085552322176766001})\approx 59.059059223$$

Steps Using Definition of Logarithm

Divide both sides by 5.54.

$$\frac{10}{5.54}=e^{0.01x}$$

Expand \frac{10}{5.54} by multiplying both numerator and the denominator by 100.

$$\frac{1000}{554}=e^{0.01x}$$

Reduce the fraction \frac{1000}{554} to lowest terms by extracting and canceling out 2.

$$\frac{500}{277}=e^{0.01x}$$

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

$$e^{0.01x}=\frac{500}{277}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.01x})=\log(\frac{500}{277})$$

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

$$0.01x\log(e)=\log(\frac{500}{277})$$

Divide both sides by \log(e).

$$0.01x=\frac{\log(\frac{500}{277})}{\log(e)}$$

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

$$0.01x=\log_{e}\left(\frac{500}{277}\right)$$

Multiply both sides by 100.

$$x=\frac{\ln(\frac{500}{277})}{0.01}$$

Solve for x (complex solution)

$$x=\ln(\frac{788860905221011805411728565282786229673206435109023004770278930664062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{17700148354958811197049631856692489668047119251071967293590862465287624612244991691538040557195928283779646387164477206241990791955440628457965897872597303746777718964761302600178359096074101138450296604892200209625205282428068085552322176766001})+i\times 200\pi n_{1}$$

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