Question

log 27 base 9-log9 base 27

Answer 1

Answer:

Step-by-step explanation:

log y base a = x implies y=a^x.

log 27 base 9 = x.

27=9^x.

3^3=3^2x.

3=2x bases are equal.

x=3/2.

log 9 base 27 = y.

9 = 27^y

3^2=3^3y

2=3y bases are equal  

y = 2/3

log 27 base 9 - log 9 base 27  

=> x - y

=> 3/2 - 2/3

=> 9-4/6

=> 5/6 (or) 0.83

Answer 2

Given : log₉27 - log₂₇9

To Find :   Simplify

Solution:

log₉27 - log₂₇9

logₐb = log b/loga

log₉27 = log 27 /log 9

log₂₇9  =  log 9 /log 27

27 = 3 x 3 x 3 = 3³

9 = 3 x 3 = 2²

log aⁿ =  n log a

log 27  = log ( 3³ )  = 3 log 3

log 9 = log ( 3²) = 2 log 3

=  3 log 3/2 log 3  -  2 log 3 /3 log 3

= 3/2  - 2/3

= (9 - 4)/6

= 5/6

log₉27 - log₂₇9  = 5/6

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