If 55-x = 2x-5, find the value of x . ?

If 5^5-x = 2^x-5, find the value of x . ?

1. 5
2. 0
3. 1
4. Can't be determined

Correct Option: A

∵ 5^5-x = 2^x-5
⇒ 5^5-x = 2^-(5-x)
⇒ (5-x)log 5 = -(5-x)log 2
⇒ (5-x)log 5 + (5-x)log 2 = 0
⇒ (5-x){log 5 + log 2 } = 0
⇒ (5-x){log10/2 + log 2 } = 0
⇒ (5-x){log10 - log 2 + log 2} = 0
⇒ 5-x = 0
∴ x = 5

Logarithm

Aptitude

Correct Option: A