有一條log的數不識做

log 9 / log 4
= 2 log 3 / 2 log 2
= log 3 / log 2
Let 2^( log 9 / log 4 ) = y,
log y = ( log 9 / log 4 )( log 2 )
log y = ( log 3 / log 2 )( log 2 )
log y = log 3
y = 3
Therefore 2^( log 9 / log 4 ) = 3

設 x = 2^(log9/log4) 就好易做啦

log(x) = log(2^(log9/log4)) = (log9)/(log4) x log(2) = 2log(3) * log(2) / (2log(2)) = log(3)

Therefore x = 3.

2^(log9/log4)
= 2^(log(3^2) / log(2^2))
= 2^( 2log(3) / 2log(2) )
= 2^( log(3)/log(2) )
= 2^( log2(3) ) ... log2(3) means log of 3 in base of 2
= 3

Usally, we use log(x) indicates log of x in base of 10.