Question

Log (21)
$log(27) \div log(9)$
÷ log 9​

Answer 1

Given : log 27  ÷ log 9

To Find :   Simplify

Solution:

log 27  ÷ log 9

27 = 3 x 3 x 3 = 3³

9 = 3 x 3 = 2²

= log ( 3³ ) ÷ log ( 3²)

log aⁿ =  n log a

log ( 3³ )  = 3 log 3

log ( 3²) = 2 log 3

=  3 log 3  ÷ 2 log 3

Cancelling  log 3 from numerator and denominator

= 3 ÷ 2

= 3/2

log 27  ÷ log 9  = 3/2 = 1.5

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