Question

if log ab^3 = log a^2b = 1 then the value of log ab is​
for class 11 IIT JEE

Answer 1

Step-by-step explanation:

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Answer 2

$Answer \: \\ \\ log_{10}(ab {}^{3} ) = 1 \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: \: log_{10}(a {}^{2} b) = 1 \\ \\ log_{10}(a {}^{3}b ) = log_{10}(10) \\ \\ log_{10}( a {}^{3}b ) - log_{10}(10) = 0 \\ \\ log_{10}( \frac{a {}^{3} b}{10} ) = 0 \\ \\ \frac{a {}^{3}b }{10} = 10 {}^{0} \\ \\ a {}^{3} b = 10 \: \: \: ....Equation \: \: \: i \\ \\ log_{10}(a {}^{2}b ) = 1 \\ \\ log_{10}(a {}^{2}b ) = log_{10}(10) \\ \\ log_{10}( \frac{a {}^{2} b}{10} ) = 0 \\ \\ a {}^{2} b = 10 \: \: ....Equation \: \: \: ii \\ \\ from \: Equation \: \: i \: and \: ii \: we \: have \\ \\ a = 1 \: \: \: \: and \: \: \: \: b \: = 10 \\ \\ log_{10}(ab) = log_{10}(a) + log_{10}(b) \\ \\ log_{10}(ab) = log_{10}(1) + log_{10}(10) \\ \\ log_{10}(ab) = 0 + 1 \\ \\ log_{10}(ab) = 1 \\ \\ therefore \: \: \: log_{10}(ab) = 1$