Question 1204250
.
{{{highlight(highlight(First))}}},  the problem in the post is written incorrectly.
The correct formulation is as follows


<pre>
    Let x be a real number such that {{{625^x}}} = 64.

    Then  {{{125^x}}} = {{{a*sqrt(b)}}}.  Find "a" and "b".
</pre>


{{{highlight(highlight(Second))}}}, &nbsp;the &nbsp;" solution " &nbsp;by &nbsp;@MathLover1 is &nbsp;TOTALLY &nbsp;WRONG.

I came to bring a correct solution.


<pre>
              {{{highlight(highlight(SOLUTION))}}}


We are given  {{{625^x}}} = 64.

It is the same as to write

    {{{5^(4x)}}} = 64.    (1)


Then

    {{{125^x}}} = {{{5^(3x)}}} = {{{(5^(4x))^(3/4)}}} = now replace  {{{5^(4x)}}}  by  64,  based on  (1)  = 64^(3/4) = 8^(3/2) = {{{8*sqrt(8)}}}.


Thus the problem is just solved.  a = 8;  b = 8.     <U>ANSWER</U>



              {{{highlight(highlight(CHECK))}}}


If 625^x = 64,  then  x*log(625) = log(64), x = {{{log((64))/log((625))}}} = 0.646014837  (approximately).


Next,  {{{125^x}}} = {{{125^0.646014837}}} = 22.627417 (approximately);   

       {{{8*sqrt(8)}}} = 22.627417  (the same value).   Check is completed and confirms the answer.
</pre>

Solved.



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For safety of your mind, simply ignore the post by @MathLover1.


Observing her activity at this forum during years, I learned that she DOES NOT know Math, at all 
(except of very local pieces).


Her method to work at this forum is to re-write from other tutors or from web-sites 
(if she find an appropriate source) - without any reference, naturally.


If she does not find the source to re-write from, she writes any gibberish,
without hesitation.



What others think about her creations, she doesn't care.



Such "tutors" should not be allowed approaching to Math education closer than a cannon shot.