The correct option is C log(2/3) 4^x 1 (9^x 1)x(4^x+9^x) Apply Lhospoitals rule= 12(log4 log9) = log23 ...

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Conversion of Numbers Using Logarithms

limx→ 04x-9x/...

Question

$lim x \to 0 \frac{4^{x} - 9^{x}}{x (4^{x} + 9^{x})}$ =

log (\frac{3}{2})

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log (\frac{2}{3})

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log (\frac{4}{3})

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log 2

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Solution

The correct option is C $log (\frac{2}{3})$

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

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