Exponential equation

Find x, if 625 ^ x = 5

The equation is exponential because the unknown is in the exponential power of 625

Result

x =  0.25

Solution:

625x=5 625=54 (54)x=5 xln⁡(625)=ln⁡(5) x=ln⁡(5)/ln⁡(625)=14=0.25625^x=5 \ \\ 625=5^4 \ \\ (5^4)^x=5 \ \\ x \ln(625)=\ln(5) \ \\ x=\ln(5) / \ln(625)=\dfrac{ 1 }{ 4 }=0.25

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