Simplify 1-log 5-1-3log1-2-log x-1-3log 5

1 log 5 =1/3 ( log 1/2+log x+1/3log 5 ) log 10 log 5 =1/3log 1/2+1/3log x +1/9log 5 log 10/5=log (1/2)^1/3+log x^1/3+log x^1/9 log 2 log (1/2)^1/3 log 5^1/ ...

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Standard XII

Mathematics

Logarithms

Simplify 1-lo...

Question

Simplify $1 - l o g 5 = \frac{1}{3} (l o g \frac{1}{2} + l o g x + \frac{1}{3} l o g 5)$

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Solution

$1 - l o g 5 = \frac{1}{3} (l o g \frac{1}{2} + l o g x + \frac{1}{3} l o g 5) l o g 10 - l o g 5 = \frac{1}{3} l o g \frac{1}{2} + \frac{1}{3} l o g x + \frac{1}{9} l o g 5 l o g \frac{10}{5} = l o g (\frac{1}{2})^{\frac{1}{3}} + l o g x^{\frac{1}{3}} + l o g x^{\frac{1}{9}} l o g 2 - l o g (\frac{1}{2})^{\frac{1}{3}} - l o g 5^{\frac{1}{9}} = l o g x^{\frac{1}{3}} l o g \frac{2}{(\frac{1}{2})^{\frac{1}{3}}} - l o g 5^{\frac{1}{9}} = l o g x^{\frac{1}{3}} l o g 2^{1 + \frac{1}{3}} - l o g 5^{\frac{1}{9}} = l o g x^{\frac{1}{3}} l o g 2^{\frac{4}{3}} - l o g 5^{\frac{1}{9}} = l o g x^{\frac{1}{3}}$

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Simplify 1−log5=13(log12+logx+13log5)

1−log5=13(log12+logx+13log5)log10−log5=13log12+13logx+19log5log105=log(12)13+logx13+logx19log2−log(12)13−log519=logx13log2(12)13−log519=logx13log21+13−log519=logx13log243−log519=logx13

Simplify $1 - l o g 5 = \frac{1}{3} (l o g \frac{1}{2} + l o g x + \frac{1}{3} l o g 5)$