5.5.3 Indices and Logarithms, Short Questions (Question 8 – 10)


Question 8
Solve the equation, log 9 ( x 2 ) = log 3 2

Solution:
log 9 ( x 2 ) = log 3 2 log a b = log c b log c a log 3 ( x 2 ) log 3 9 = log 3 2 log 3 ( x 2 ) 2 = log 3 2 log 3 ( x 2 ) = 2 log 3 2 log 3 ( x 2 ) = log 3 2 2 x 2 = 4 x = 6



Question 9
Solve the equation, log 9 ( 2 x + 12 ) = log 3 ( x + 2 )

Solution:
log 9 ( 2 x + 12 ) = log 3 ( x + 2 ) log 3 ( 2 x + 12 ) log 3 9 = log 3 ( x + 2 ) log 3 ( 2 x + 12 ) = 2 log 3 ( x + 2 ) log 3 ( 2 x + 12 ) = log 3 ( x + 2 ) 2 2 x + 12 = x 2 + 4 x + 4 x 2 + 2 x 8 = 0 ( x + 4 ) ( x 2 ) = 0 x = 4  (not accepted) x = 2



Question 10
Solve the equation, log 4 x = 3 2 log 2 3

Solution:
log 4 x = 3 2 log 2 3 log 2 x log 2 4 = 3 2 log 2 3 log 2 x 2 = 3 2 log 2 3 log 2 x = 2 × 3 2 log 2 3 log 2 x = 3 log 2 3 log 2 x = log 2 3 3 x = 27


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