SOLUTION: I need help with these questions 5^x=125 8^x+1=16^x 81^(3/4)=x 8^(-2/3)=x

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Question 492608: I need help with these questions
5^x=125
8^x+1=16^x
81^(3/4)=x
8^(-2/3)=x
Found 2 solutions by lwsshak3, MathTherapy:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solving for x:
..
5^x=125
5^x=5^3
x=3
..
8^x+1=16^x
don't know how to do the algebra on this one.
My graphing program gives and answer of x=.464968..
..
81^(3/4)=x
Take the 4th root of 81 and cube it
81^(1/4)=3
3^2=9
x=9
..
8^(-2/3)=x
Take the cube root of 8 and raise it to -2 power
8^1/3=2
2^-2=1/2^2=1/4
x=1/4

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with these questions
5^x=125
8^x+1=16^x
81^(3/4)=x
8^(-2/3)=x
==========
Other PERSON'S response:
.
8^x+1=16^x
don't know how to do the algebra on this one.
My graphing program gives and answer of x=.464968..
===
This AUTHOR'S response to the above:
       8^x+1=16^x
    8%5E%28x+%2B+1%29+=+16%5Ex
 %282%5E3%29%5E%28x+%2B+1%29+=+%282%5E4%29%5Ex
 2%5E%283%28x+%2B+1%29%29+=+2%5E%284x%29
   3(x + 1) = 4x --- EQUATING exponents, since bases are equal
     3x + 3 = 4x
          3 = 4x - 3x
         highlight%283+=+x%29

It appears as though the person interpreted this as: 8%5Ex+%2B+1+=+16%5Ex
==============
Other PERSON'S response:
..
81^(3/4)=x
Take the 4th root of 81 and cube it
81^(1/4)=3
3^2=9
x=9
===
This AUTHOR'S response to the above:
CUBING the 4th root of 81 doesn't result in 3%5E2+=+9, but 3%5E3+=+27 instead!!
So, the CORRECT answer is 27, NOT 9.