Solve the given equation. (125^frac (1)/(5))(5^(x)/(5))=1 x=square (Type an integer or a fraction )

To solve the equation, we need to simplify the expression and isolate the variable x.<br /><br />Given equation: $\frac {125^{\frac {1}{5}}}{5^{\frac {x}{5}}}=1$<br /><br />Step 1: Simplify the numerator and denominator separately.<br />$125^{\frac {1}{5}} = 5$<br />$5^{\frac {x}{5}} = 5^{\frac {x}{5}}$<br /><br />Step 2: Rewrite the equation with the simplified numerator and denominator.<br />$\frac {5}{5^{\frac {x}{5}}}=1$<br /><br />Step 3: Multiply both sides of the equation by $5^{\frac {x}{5}}$ to eliminate the denominator.<br />$5 = 5^{\frac {x}{5}}$<br /><br />Step 4: Take the logarithm of both sides of the equation to solve for x.<br />$\log_5(5) = \log_5(5^{\frac {x}{5}})$<br />$1 = \frac {x}{5}$<br />$x = 5$<br /><br />Therefore, the solution to the equation is $x = 5$.