MHB Need help solving this logarithmic problem

[Sharpy1]

(e^3x)(e⁴)^x = e^4x -15

Could use help solving this here within the next 40 minutes, appreciate the help, this is the last one out of a 75 question take home test and I'm having soo many issues.

Thanks in advanced for the help.

 

[MarkFL]

Hello and welcome to MHB!:

Has your professor given you permission to get outside help with this graded assignment?

 

[Sharpy1]

Yes only for 3 questions and we have to post where we got the outside help from.

 

[MarkFL]

Okay, we are given:

$$e^{3x}\cdot \left(e^4 \right)^x=e^{4x}-15$$

I would first use the property of exponents $$\left(a^b \right)^c=a^{bc}$$ on the second factor on the left, and so we have:

$$e^{3x}\cdot e^{4x}=e^{4x}-15$$

What do we get when we apply the property $$a^b\cdot a^c=a^{b+c}$$ on the left?

 

[Sharpy1]

I have it now, I was reading it as e^4x-15 not e^4x-15

Thanks for the help everyone

 

[MarkFL]

Your original interpretation has no real solutions. Glad you figured it out. :D