Question

Show that:
$\log \frac{50}{147} = \log 2 + 2\log 5 - \log 3 - 2\log 7$

Answer 1

concepts : $log(AB)=logA+logB$......(1)

$log\frac{A}{B}=logA-logB$........(2)

$logA^n=nlogA$.......(3)


LHS = log {50/147}

= log{ (2 × 5 × 5)/{3 × 7 × 7)}

= log{ (2 × 5²)/(3 × 7²)}

= log(2 × 5²) - log(3 × 7²) [ using formula (2), ]

= log2 + log5² - [ log3 + log7² ] [ using formula (1), ]

= log2 + 2log5 - log3 - 2log7 [using formula (3), ]

hence, $\log \frac{50}{147} = \log 2 + 2\log 5 - \log 3 - 2\log 7$