Question

if log27 base12 =a then log16 base6=

Answer 1

hi friend,

log₁₂ 27=a

a = [ log₆ ( 3³ ) ] / ( log₆ 12 )

a = 3 [ log₆ (6/2) ] / [ log₆ ( 6 x 2 ) ]

a = 3 [ ( log₆ 6 ) - ( log₆ 2 ) ] / [ ( log₆ 6 ) +( log₆2)]

a = 3 ( 1 - log₆ 2 ) / ( 1 + log₆ 2 )

a(1+log₆ 2)=3-3(log₆ 2)

a+a log₆ 2=3-3(log₆ 2)

a (log₆ 2) +3(log₆ 2)=3-a

(a+3) log₆ 2 = 3-a

log₆ 2 =(3-a)/(3+a)

We have to find the value of log₆ 16

log₆ 16=log₆ ( 2⁴ )

log₆ 16=4 log₆ 2

log₆ 16=4[(3-a)/(3+a)]

or

log₆ 16=12-4a/3+a

hope it helps you

Answer 2

Hi friend,

I have attached 5 pics

Ans is 12-4a/3+a

4(3-a)/3+a = 12-4a/3+a
Hope helped