Writing the equation in exponential form gives us x^52 = (x^12)^5 = 32 = 2^5. Solving x^12 = 2 gives us x = 4.

jmc

algebra intermediate

Problem

Find

x

lo g_{x} 32 = \frac{5}{2}

Solution

Writing the equation in exponential form gives us

x^{\frac{5}{2}} = (x^{\frac{1}{2}})^{5} = 32 = 2^{5}

. Solving

x^{\frac{1}{2}} = 2

gives us

x = 4

Final answer