Question 492608
<pre>
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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Other PERSON'S response:
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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..
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This AUTHOR'S response to the above:
       8^x+1=16^x
    {{{8^(x + 1) = 16^x}}}
 {{{(2^3)^(x + 1) = (2^4)^x}}}
 {{{2^(3(x + 1)) = 2^(4x)}}}
   3(x + 1) = 4x --- EQUATING exponents, since bases are equal
     3x + 3 = 4x
          3 = 4x - 3x
         {{{highlight(3 = x)}}}

It appears as though the person interpreted this as: {{{8^x + 1 = 16^x}}}
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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
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This AUTHOR'S response to the above:
CUBING the 4th root of 81 doesn't result in {{{3^2 = 9}}}, but {{{3^3 = 27}}} instead!!
So, the CORRECT answer is <font color = red><font size = 4><b>27</font></font></b>, NOT 9.</pre>