33554432=x^5

33554432=x^5   x = ?

$$\small{\text{$ \rm{The~prime~ factorization~ of~} \mathbf{ 33554432 = 2^{25} } $}} \\ \small{\text{$ \rm{so~we~have~} \mathbf{ 2^{25} = x^5} $}} \\ \small{\text{$ \rm{or~} \mathbf{ 2^{5\cdot 5} = x^5} $}} \\ \small{\text{$ \rm{or~} \mathbf{ (2^5)^5 = (x)^5} \qquad | \qquad \rm {comparing~coefficient} $}} \\ \small{\text{$ \rm{so~} \mathbf{ (2^5) = x} $}} \\ \small{\text{$ \rm{or~} \mathbf{ 32 = x} $}} \\$$

Raise each side to te power of 1/5

Hallo anonymous!

33554432=x^5

ln 33554432  = 5 * ln x

Thanks asinus 

You have done it the really long way.  You only need to use logs when you are finding a power.

The best way to do this problem is to just raise both sides to the power of 1/5

$$\\33554432=x^5\\\\ x^5=33554432\\\\ (x^5)^{1/5}=33554432^{1/5}\\\\ x=33554432^{1/5}\\\\$$

$${{\mathtt{33\,554\,432}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right)} = {\mathtt{32}}$$