SOLUTION: How do I solve these two logarithms. I have the problems 5 ^x-1/3 = power 3 square root of 5 (the 3 is small and on top of the square root) and log (base 4) (x-2) + lo

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I solve these two logarithms. I have the problems 5 ^x-1/3 = power 3 square root of 5 (the 3 is small and on top of the square root) and log (base 4) (x-2) + lo      Log On


   

Question 895258: How do I solve these two logarithms.
I have the problems
5 ^x-1/3 = power 3 square root of 5 (the 3 is small and on top of the square root)
and
log (base 4) (x-2) + log (base 4) (x+1) =1
I would like some help with the steps that I could go about solving these logs
thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
5 ^x-1/3 = power 3 square root of 5 (the 3 is small and on top of the square root)

5%5Ex-1%2F3=%28sqrt%285%29%29%5E3
5%5Ex=1%2F3%2Bsqrt%285%29sqrt%285%29sqrt%285%29
5%5Ex=1%2F3%2A5%2A5%5E%281%2F2%29

Decimal approximation for the right member, and then table of common logarithms or calculator to continue.

5%5Ex=11.5136732208
x%2Alog%2810%2C5%29=log%2810%2C11.5136732208%29
x%2A0.6989700=1.06121389921
x=1.51825

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How do I solve these two logarithms.
I have the problems
5 ^x-1/3 = power 3 square root of 5 (the 3 is small and on top of the square root)
and
log (base 4) (x-2) + log (base 4) (x+1) =1
I would like some help with the steps that I could go about solving these logs
thank you


If 5%5Ex+-+1%2F3+=+root+%283%2C+5%29? Then highlight_green%28x+=+0.443988%29



log+%284%2C+%28x+-+2%29%29+%2B+log+%284%2C+%28x+%2B+1%29%29+=+1

highlight_green%28x+=+3%29

OR

x = - 2 (ignore,as this is an EXTRANEOUS solution)

You can do the check!! 



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