Question

Please solve this question :

Answer 1

It's done.I hope u will understand the steps.

Answer 2

Given ⇒
 $log \sqrt[3]{ \frac{56}{9} }$ = 1/3 [ log 7 - 2log 3] + log 2.

From L.H.S.
$log \sqrt[3]{ \frac{56}{9} }$  = $\frac{1}{3} log {\frac{56}{9} }$ [∵ log aⁿ = n loga]

 = 1/3 log 56 - 1/3 log 9
[nlog(a/b) = nloga - nlog b]

 = 1/3 log (2 × 2 × 2 × 7) - 1/3 log 9
 = 1/3 log (2³ × 7) - 1/3 log 3²
[∵ log (a × b) = log a + log b]

 = 1/3 log 2³ + 1/3 log 7 - 2/3 log 3
 = log 2 + 1/3 log 7 - 2/3 log 3
 = log 2 + 1/3[log 7 - 2 log 3] 
 = 1/3 [log 7 - 2 log 3] + log 2
 = R.H.S.

∵ L.H.S. = R.H.S.

Hence Proved.


Hope it helps.