Question 891480
5^x^2 = 2^5x
<pre>
I can't tell whether that means

{{{(5^x)^2}}}{{{""=""}}}{{{2^(5x)}}} or {{{matrix(2,1,"",5^(x^2))}}}{{{matrix(2,1,"",""="")}}}{{{matrix(2,1,"",2^(5x))}}}

If it's the first way:

{{{5^(2x)}}}{{{""=""}}}{{{2^(5x)}}}

{{{ln(5^(2x))}}}{{{""=""}}}{{{ln(2^(5x))}}}

{{{2x*ln(5)}}}{{{""=""}}}{{{5x*ln(2)}}}

{{{2x*ln(5)}}}{{{""-""}}}{{{5x*ln(2)}}} {{{""=""}}} {{{"0"}}}

{{{x(2ln(5)+5ln(2))}}}  {{{""=""}}} {{{"0"}}}

Divide both sides by {{{2ln(5)+5ln(2)}}}

{{{x}}}{{{""=""}}}{{{"0"}}}

------------------------

If it's the second way,

{{{matrix(2,1,"",5^(x^2))}}}{{{matrix(2,1,"",""="")}}}{{{matrix(2,1,"",2^(5x))}}}

{{{matrix(2,1,"",ln(5^(x^2)))}}}{{{matrix(2,1,"",""="")}}}{{{matrix(2,1,"",ln(2^(5x)))}}}

{{{(x^2)ln(5)}}}{{{""=""}}}{{{5x*ln(2)}}}

{{{(x^2)ln(5)}}}{{{""-""}}}{{{5x*ln(2)}}}{{{""=""}}}{{{"0"}}}

{{{x*(x*ln(5)-5ln(2))}}}{{{""=""}}}{{{"0"}}}

{{{x=0}}};  {{{x*ln(5)-5*ln(2)=0}}}

          {{{x*ln(5)=5*ln(2)}}}

          {{{x=5*ln(2)/ln(5)}}}

          {{{x=2.15338279}}}

Answers:   0, 2.1534 (rounded to four decimal places).

Edwin</pre>