# Quantitative Aptitude – Algebra – Logarithms – If x is a positive quantity such that 2^x ## Slot -1 – Quantitative Aptitude – Algebra – Logarithms – If x is a positive quantity such that 2^x

If x is a positive quantity such that 2^x = 3^log(base5)^⁡2 , then x is equal to?

a) log(base5⁡)^9
b) 1 + log(base5)⁡ 3/5
c) log(base5⁡)^8
d) 1 + log(base3) ⁡5/3

Answer: b) 1 + log(base5)⁡ 3/5

Solution:
Given , 2^x = 3^log(base5)⁡2
taking log of both sides ,
x log⁡2 = log(base5) 2 log⁡ 3 = (log⁡ 2 log⁡ 3 )/log⁡5
Or x = log 3/log⁡ 5 = log(base5)⁡ 3 = 1+ log(base5)⁡ 3/5

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