Write as a single logarithm: log32/log2

Question

Write log32/log2 as a single logarithm

Answer 1

Note that 32 = 2⁵.  We also use the property log(a^b) = b·log(a):

 

log(32)/log(2) = log(2⁵)/log(2)  = 5·log(2)/log(2) = 5

Answer 2

By the change of base formula, log_ab = logb/loga

 

So, log₂32 = log32/log2

Answer 3

log32/log2 = ?

 

32 = 2⁵

 

log32/log2 = log(2⁵)/log2 = (5 log2)/log2 = 5