MHB Need help solving this logarithmic problem

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The logarithmic problem presented is e^(3x) * (e^4)^x = e^(4x) - 15. The discussion involves applying properties of exponents to simplify the equation. After rewriting the left side as e^(3x + 4x), it becomes clear that the original interpretation was incorrect, leading to no real solutions. The participant successfully clarified their understanding of the equation. The conversation highlights the importance of correctly interpreting exponential expressions in solving logarithmic equations.
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(e3x)(e4)x = e4x -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.
 
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Hello and welcome to MHB!:

Has your professor given you permission to get outside help with this graded assignment?
 
Yes only for 3 questions and we have to post where we got the outside help from.
 
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?
 
I have it now, I was reading it as e4x-15 not e4x-15

Thanks for the help everyone
 
Your original interpretation has no real solutions. Glad you figured it out. :D
 
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