Logarithms-17

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Find x , if : (i) log 10 (x + 5) = 1

(ii) log 10 (x + 1) + log 10 (x - 1) = log 10 11 + 2 log 10 3

Solution:

(i) log 10 (x + 5) = 1 = log 10 10

=> (x + 5) = 10

=> x = 5

(ii)log 10 (x + 1) + log 10 (x - 1) = log 10 11 + 2 log 10 3

=> log 10 (x + 1) (x - 1) = log 10 11 + log 10 3 2

=> log (x 2 - 1) = log (11 X 9)

=> x 2 - 1 = 99

Therefore, x 2 = 100

=> x = 10

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