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Find x if \(\log_x32 = \dfrac{5}{2}\).

 Jul 16, 2019
 #1
avatar+102386 
+1

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

 

 

cool cool cool

 Jul 16, 2019
 #2
avatar+102386 
+1

An easier - and more straightforward -  way to do this

 

log x   32  = 5/2

 

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

 

 

 

cool cool cool

 Jul 16, 2019
edited by CPhill  Jul 16, 2019

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