(i)Find the real value of 'x' satisfying the equation 
(ii)Solve for x : 
(iii)Solve for x : 
= 
(iv)Find the product of roots of the equation
(log 3 x) 2 – 2(log 3 x) – 5 = 0
(v)Find sum of roots of the equation 4 x – 7.2 x + 6 = 0
Text Solution
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(i) 
= 2
⇒ 
= 2
⇒ x 2 – x = 2 ⇒ x 2 – x – 2 = 0 ⇒ (x – 2)(x + 1) = 0
⇒ x = 2, x = –1 but x > 0 and x 2 – x = 0 ⇒ x(x – 1) > 0
x ∈ (– ∞, 0 ) ∪ (1, ∞ )
(ii) 
x = 10 or log 10 x + 2 = 0 ⇒ x = 10 –2 = 
(iii) 
= 
; 
log x = 5 + log x
log 2 x + 2 log x – 15 = 0 ; (log x + 5)(log x – 3) = 0
log x = –5, log x = 3 ; x = 10 –5 , x = 10 3 .
(iv) t 2 – 2t – 5 = 0
sum of roots = 2
log 3 x 1 + log 3 x 2 = 2 ⇒ log 3 (x 1 x 2 ) = 2 ⇒ x 1 x 2 = 3 2 = 9
(v) (2 x ) 2 – 7(2 x ) + 6 = 0
⇒ t 2 – 7t + 6 = 0
t = 1, t = 6
Roots 2 x = 1, 2 x = 6
⇒ x = 1, x = log 2 6
Product of roots = (1)(log 2 6) = log 2 6
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