logarithmic functions

if you mean 5^x = sqrt(5) then:

x = 1/2

Because square roots are numbers raised to the 1/2 power.

Hope that helped

$5^x = \sqrt5\\ x \log 5 = \log (\sqrt5)\\ x = \dfrac{\log(\sqrt5)}{\log 5}$

Put this into the calculator and it is 1/2.

start by taking the log on both sides of the equation.

lg5(5^x) = lg5(sqr(5))

x = 1/2