Solving an exponential equation

[gamaz321]

I am trying to find the solution to an exponential equation. However, after a few steps, I cannot figure out to move further. I would appreciate any suggestions to help me retry the problem again.
Thank you.

 

[topsquark]

I am trying to find the solution to an exponential equation. However, after a few steps, I cannot figure out to move further. I would appreciate any suggestions to help me retry the problem again.
Thank you.

Hmmmmm... Ugly. Is this the whole problem or just where you are getting lost? It seems a strange starting point.

-Dan

 

[gamaz321]

The problem is stated in the first line after Solve for x statement. I could proceed in just a couple few steps. I got stuck after I did my second step where I have no clue as to how to move further. I am not even sure if my approach is correct or not. Thank you.

 

[Dr.Peterson]

The problem is stated in the first line after Solve for x statement. I could proceed in just a couple few steps. I got stuck after I did my second step where I have no clue as to how to move further. I am not even sure if my approach is correct or not. Thank you.

Can you show us an image of the actual problem? I'm wondering if what you take as [imath]\log_{1/4}(x-1)[/imath] is really [imath]\log_{1/4}(x)-1[/imath], which would be easier to handle.

 

[gamaz321]

Here is the image of the actual problem. Hope it helps.

 

[BigBeachBanana]

Here is the image of the actual problem. Hope it helps.

View attachment 33748

I agree with @Dr.Peterson's interpretation of the problem, otherwise, it cannot be solved algebraically.
Move the -1 to the front of the log to make it less ambiguous.

[math]\huge 5^{1+\log_{4}x}+5^{-1+\log_{1/4}x}=\frac{26}{5}[/math]

 

[gamaz321]

OK, thanks. I am going to work on this modified problem.