Question

Evaluate:
$\log_{10} \big(\frac{351}{539} \big) +2 \log_{10} \big(\frac{91}{110} \big) - 3\log_{10} \big(\frac{39}{110} \big)$

Answer 1

Please see the attachment

Answer 2

Solution :

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We know the logarithmic laws:

i ) log(xy) = logx + logy

ii ) log(x/y) = logx - logy

iii ) nlogm = logmⁿ

iv ) logx( base x ) = 1

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$\log_{10} \big(\frac{351}{539} \big) +2 \log_{10} \big(\frac{91}{110} \big) - 3\log_{10} \big(\frac{39}{110} \big)$

= log(351/539) + log(91/110)² - log(39/110)³

= log[(351/539)(91/110)²]/[(39/110)³]

After cancellation, we get

= log10(base 10)

= 1