Alex C.

asked • 07/15/16

Logs, solving for x

Hi,I need help solving for x for : 
 
logx2 (101) = logx+1 (101) 
 
The bases are not the same so im guessing you have to use change of base formula right? Im not sure though how to use it for a problem like this. 

1 Expert Answer

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Mark M. answered • 07/15/16

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Not that complicated.
The exponents are equal (log = log) , and the results are equal (101 = 101).
Therefore the bases are equal.
x2 = x + 1
x2 - x - 1 = 0
 
Use the Quadratic formula to solve for x.
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Alex C.

What about ln(x)-log(x)=1 ?
 
The base for ln is e and log is 10 , so in this situation do I do the change of base property?
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07/15/16

Mark M.

I worked with change of base. Yuck! Value of x must be irrational.
I might be missing something and shall mull over this for a while.
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07/15/16

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