If a -log 10 2 and b -log 10 3- then log 10-108 can be written as-A- 2 a -3 b -5B- 2 a -3 bC- a -3 b -5D- a -3 b

The correct option is A 2a+3b/5log_10√(108) = nbsp;log_10(108)^1/5 = 1/5 log_10108 = 1/5 log_10(2^2 × 3^3) = 1/5 (log_102^2 + log_103^3) = 1/5 ( 2log_102 ...

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Byju's Answer

Standard IX

Mathematics

Logarithms

If a =log 10 ...

Question

If $a = l o g_{10} 2$ and $b = l o g_{10} 3$ , then $l o g_{10} \sqrt[5]{108}$ can be written as .

\frac{2 a + 3 b}{5}

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2 a + 3 b

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\frac{a + 3 b}{5}

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a + 3 b

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Solution

The correct option is A $\frac{2 a + 3 b}{5}$
$l o g_{10} \sqrt[5]{108} = l o g_{10} (108)^{\frac{1}{5}} = \frac{1}{5} l o g_{10} 108 = \frac{1}{5} l o g_{10} (2^{2} \times 3^{3}) = \frac{1}{5} (l o g_{10} 2^{2} + l o g_{10} 3^{3}) = \frac{1}{5} (2 l o g_{10} 2 + 3 l o g_{10} 3) = \frac{2 a}{5} + \frac{3 b}{5}$

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If a=log102 and b=log103, then log105√108 can be written as .

The correct option is A 2a+3b5log105√108=log10(108)15=15 log10108=15 log10(22×33)=15 (log1022+log1033)=15( 2log102+3log103)=2a5+3b5

If $a = l o g_{10} 2$ and $b = l o g_{10} 3$ , then $l o g_{10} \sqrt[5]{108}$ can be written as .