Given log 10 x = 2a and log 10 y = . (i) Write 10 a in terms of x. (ii) Write 10 2b + 1 in terms of y. (iii) If log 10 P = 3a - 2b, express P in terms of x and y.

(i) Given, ⇒ log 10 x = 2a ⇒ x = 10 2a ⇒ x = (10 a ) 2 Taking square root on both sides, we get : Hence, 10 a = . (ii) Given, ⇒ 10 2b + 1 ⇒ 10 2b .10 1 .........(1) Given, Substituting value of 10 2b from equation (2) in equation (1), we get : ⇒ y 4 .10 1 ⇒ 10y 4 . Hence, 10 2b + 1 = 10y 4 . (iii) Given, ⇒ log 10 P = 3a - 2b ⇒ P = 10 3a - 2b ⇒ P = 10 3a .10 -2b ⇒ P = We know that: (shown above) y 4 = 10 2b and = 10 a ∴ P = = . Hence, P =

Mathematics

Given log10 x = 2a and log10 y = . (i) Write 10a in terms of x. (ii) Write 102b + 1 in terms of y. (iii) If log10P = 3a - 2b, express P in terms of x and y.

Logarithms

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Mathematics

Given log<sub>10</sub> x = 2a and log<sub>10</sub> y = . (i) Write 10<sup>a</sup> in terms of x. (ii) Write 10<sup>2b + 1</sup> in terms of y. (iii) If log<sub>10</sub>P = 3a - 2b, express P in terms of x and y.

Logarithms

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Mathematics

Given log<sub>10</sub> x = 2a and log<sub>10</sub> y = . (i) Write 10<sup>a</sup> in terms of x. (ii) Write 10<sup>2b + 1</sup> in terms of y. (iii) If log<sub>10</sub>P = 3a - 2b, express P in terms of x and y.

Logarithms

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Solve :
log₅ (x + 1) - 1 = 1 + log₅ (x - 1).