Question

Question of log 50 points
Hint(take log 7 with x as t)​

Answer 1

Sol: 2 logx 7 + log7x 7 +3 log49x 7 = 0 ⇒ 2 (log7 7/ log7 x) + (log7 7/log7 7x) + 3 (log7 7/log7 7) = 0 [logb a = logk a / logk b] ⇒ 2 (1/ log7 x) + (1/log7 7x) + 3 (1/log7 49x) = 0 [loga a = 1] ⇒ 2/ log7 x + 1/(log7 7 + log7 x) + 3/(log7 49 + log7 x) = 0 ⇒ 2/ log7 x + 1/(1 + log7 x) + 3/(2 + log7 x) = 0 Let log7 x be a. ⇒ 2/a + 1/(1+a) + 3/(2+a) = 0 By taking LCM and cross multiplication. ⇒ 2(1 + a)(2 + a) + a(2 + a) + 3a(1 + a) = 0 ⇒ 2(a2 + 3a + 2) + (2a + a2) + (3a + 3a2) = 0 ⇒ 6a2 + 11a + 4 = 0 ⇒ (3a + 4)(2a + 1) = 0 If 3a + 4 = 0 3a = -4 a = -4/3 ⇒ log7 x = -4/3 ⇒ x = 7(-4/3) If 2a + 1 = 0 2a = -1 a = -1/2 ⇒ log7 x = -1/2 ⇒ x = 7(-1/2) Hence, the values of x are 7(-4/3) or 7(-1/2).

Answer 2

Answer:

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