Question 1148840
sqrt(125^x) = 5/(25^x)
<pre>{{{matrix(1,3, sqrt(125^x), "=", 5/(25^x))}}}
{{{matrix(1,3, (sqrt(125^x))^2, "=", (5/25^x)^2)}}} --- Squaring both sides
{{{matrix(1,3, 125^x, "=", 5^2/25^(2x))}}} 
{{{matrix(1,3, (5^3)^x, "=", 5^2/(5^2)^(2x))}}} ------- Changing bases
{{{matrix(1,3, 5^(3x), "=", 5^2/5^(4x))}}} 
{{{matrix(1,3, 5^(3x), "=", 5^(2 - 4x))}}} 
3x = 2 - 4x ------ Equating exponents, since their bases are equal
3x + 4x = 2
7x = 2
{{{highlight_green(matrix(1,3, x, "=", 2/7))}}}

<b>FYI:</b> LOGS are definitely NOT REQUIRED to solve this, as it's not that much of a COMPLEX exponents-problem. </pre>