Question

log(a+b/2)=1/2(loga+logb) show that a=b

Answer 1

Hope u like my process
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$= > \bf \: log( \frac{a + b}{2} ) = \frac{1}{2} ( log(a) + log(b) ) \\ \\ = > 2( log(a + b) - log(2) ) = log(ab) \\ \\ = > log( {(a + b)}^{2} ) - log( {2}^{2} ) = log(ab) \\ \\ = > log(a + b) ^{2} = log(ab) + log(4) \\ \\ = > log(a + b) ^{2} = log(4ab) \\ \\ = > {(a + b)}^{2} = 4ab \\ \\ = > {(a + b)}^{2} - 4ab = 0 \\ \\ = > {(a - b)}^{2} = 0 \\ \\ = > a - b = 0 \\ \\ = > \bf \: a = b...... < \: proved >$
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