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Logarithms

Given log3a...

Question

Given $l o g_{3} (a) = c$ and $l o g_{3} (b) = 2 c, a =$

3 c

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c + 3

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b^{2}

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\sqrt{b}

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\frac{b}{2}

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Solution

The correct option is C $\sqrt{b}$
Given, ${log}_{3} (a) = c$ and ${log}_{3} (b) = 2 c$
$∴ a = 3^{c}$ and $b = 3^{2 c}$
Now consider $a^{2}$ as follows:
$a^{2} = {(3}^{c})^{2}$
$\Rightarrow a^{2} = 3^{2 c}$
$\Rightarrow a^{2} = b$
$\Rightarrow a = \sqrt{b}$

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