Logarithms-20

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Given log 10 x = a and log 10 y = b

(i) Write down 10 a - 1 in terms of x

(ii) Write down 10 2b in terms of y

(iii) If log 10 P = 2a - b ; express P in terms of x and y

Solution:

(i) log 10 x = a

=> 10 a = x

Therefore, 10 a - 1 = 10 a / 10 1 = x / 10

(ii) log 10 y = b

=> 10 b = y

Therefore, 10 2b = (10 b ) 2 = y 2

(iii) log 10 P = 2a - b

log 10 P = 2 log 10 x - log y

=> log 10 P = log x 2 - log y

=> log P = log x 2 / y

Therefore, P = x 2 / y

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