Question

How do I solve : 4e ^ 0.1x = 60

Answer 1

x = 10 1n (15)

In decimal form it's 27.0805201

Answer 2

Hey Jspjulie,

Lets solve your problem step by step.

The question we are encountering is: How do I solve :
`4e^(0.1x)=60`.

The first step is to divide both sides by 4.


`(4e^(0.1x))/(4)=(60)/(4)`

Now we simplify the fraction


`e^(0.1x)=15`


`\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)`


`\ln \left(e^(0.1x)\right)=\ln \left(15\right)`

Now we have to apply the log rule:
`\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)`


`0.1x\ln \left(e\right)=\ln \left(15\right)`

Now we simplify


`0.1x=\ln \left(15\right)`

Finally, we reach our answer


`x=\ln \left(15\right)\cdot \:10`

Hope this helps,

AnthrαX