How do I find the inverse of an fractional exponential function?

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zhkhelpneeded

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I request that the person who solves this provides steps to explain how they got their answer.

The problem is y = (5^(1+x) + 1)/ (5^x)

I've tried this several times, and I've gotten answers different from the answer key. I'm not sure what I'm doing wrong.

The key says the answer should be log base 1/5 to the power of (x-5). I don't get how the base in the original problem is 5, but the inverse becomes 1/5. Can someone explain how that happens with showing steps?
 
zhkhelpneeded said:
I request that the person who solves this provides steps to explain how they got their answer.

The problem is y = (5^(1+x) + 1)/ (5^x)

I've tried this several times, and I've gotten answers different from the answer key. I'm not sure what I'm doing wrong.

The key says the answer should be log base 1/5 to the power of (x-5). I don't get how the base in the original problem is 5, but the inverse becomes 1/5. Can someone explain how that happens with showing steps?
Click to expand...
Please post your solution.
 
zhkhelpneeded said:
I request that the person who solves this provides steps to explain how they got their answer.

The problem is y = (5^(1+x) + 1)/ (5^x)

I've tried this several times, and I've gotten answers different from the answer key. I'm not sure what I'm doing wrong.

The key says the answer should be log base 1/5 to the power of (x-5). I don't get how the base in the original problem is 5, but the inverse becomes 1/5. Can someone explain how that happens with showing steps?
Click to expand...
I certainly wouldn't have used base 1/5; but that doesn't make either you, me, or the book wrong. A textbook answer doesn't mean "it must be written in this form", but merely "anything equivalent to this is correct".

Very likely your answer is correct, and can be shown to be equal. Show us what you got, and we can show how to do this.
 
zhkhelpneeded said:
I request that the person who solves this provides steps to explain how they got their answer.
Click to expand...
I agree that the person who solves this problem should provides steps to explain how they got their answer. I think that you expect that to be a helper from this forum when in fact the helpers from this forum expect it to be you who explains the solution.

This is a free math help forum and not a free homework service forum. If you had read the posting guidelines you would have know that we expect you to share the work that you have done so far with your problem so we know where you are making any mistakes and what type of hints you need to get back on track.

Please post back sharing your work and you'll receive the help you need.
 
You have \(\displaystyle y= \frac{5^{1+ x}+ 1}{5^x}\). The first thing I would is write that \(\displaystyle 5^{1+ x}\) as \(\displaystyle (5^1)(5^x)= 5(5^x)\) so the equation is \(\displaystyle y= \frac{5(5^x)+ 1}{5^x}\).

Now let \(\displaystyle u= 5^x\) so the equation becomes \(\displaystyle y= \frac{5u+ 1}{u}\).

Can you solve that for u? Once you have done that what is x?
 
Personally I would not have a made a substitution. I would just realize that y = 5 + 1/5x and go from there.
 
I don't know how to update the post, but here is my attempted solution. It is clearly very wrong.

0.png
 
zhkhelpneeded said:
I don't know how to update the post, but here is my attempted solution. It is clearly very wrong.

View attachment 24582
Click to expand...

The main error is that you took the log of only one factor on the left, and of only one term on the right. You can't do that; it has to be the log of each entire side, in order to be sure that the results are equal. There's more wrong, as well.

First isolate 5^y, and take the log last. You may find that the substitution idea helps you focus on that (isolating u); or you may find that simplifying the fraction as Jomo suggested makes the whole expression easier to handle.

But whatever way you like, try again, and just make sure that each step is one you can justify.
 
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