Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Values of x satisfying the equation log 52 x + log 5x 
= 1 are
A
1
B
5
C
D
3
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,c)
(log 5 x) 2 + log 5x 
= 1 ⇒ (log 5 x) 2 + log 5x 5 – log 5x x = 1
⇒ (log 5 x) 2 + 
– 
= 1
⇒ (log 5 x) 2 + 
– 
= 1
Let log 5 x = t
∴ t 2 + 
– 
= 1 ⇒ 
= 1 ⇒ t 3 + t 2 + 1 – t = 1 + t
t 3 + t 2 – 2t = 0 ; t(t 2 + t – 2) = 0 ; t(t – 1) (t + 2) = 0
t = 0, 1, – 2
∴ log 5 x = 0, 1, –2 ∴ x = 1, 5, 
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