Question 201772
Solve for x:
{{{(1/5)^(2x) = 625}}} Substitute {{{625 = 5^4}}}
{{{(1/5)^(2x) = 5^4}}} Substitute {{{5^4 = (1/5)^-4}}}
{{{(1/5)^(2x) = (1/5)^-4}}} If the bases ({{{1/5}}}) are equal, the exponents are equal, so...
{{{2x = -4}}} Divide both sides by 2.
{{{highlight(x = -2)}}}
Check:
{{{(1/5)^(2x) = 625}}} Substitute x = -2.
{{{(1/5)^-4 = 625}}}
{{{5^4 = 625}}}
{{{625 = 625}}} OK!