Find x if \(\log_x32 = \dfrac{5}{2}\).
log x 32 = 5/2
Using the change of base rule we have that
log 32 5
_____ = ___ rearrange as
log x 2
(2/5) log 32 = log x
This says that 10^[ (2/5)log 32 ] = x = 4
An easier - and more straightforward - way to do this
This says that
x^(5/2) = 32 take each side to the (2/5) power
x = 32^(2/5) = [ 32^(1/5) } ^2 = [ 2]^2 = 4
