Question

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

Answer 1

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. 

$\dfrac{4e^{0.1x}}{4}=\dfrac{60}{4}$ 

       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

Answer 2

X = 10 1n (15)

In decimal form it's 27.0805201