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Question 11 : If x is a positive quantity such that 2^{x} = 3^{log52} , then x is equal to

- log
_{5}9 - 1 + log
_{5}\\frac{3}{5}) - 1 + log
_{3}(\\frac{5}{3})) - log
_{5}8

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Given, 2^{x} = 3^{log52}

Taking log on both sides, we get

log (2^{x}) = log (3^{log52})

x × log(2) = log_{5}(2) × log(3)

x = \\frac{log_5 2 × log 3}{log 2})

Let us consider the base as 3,

x = \\frac{log_52 × log_3 3}{log_3 2})

x = \\frac{log_5 2 × 1}{log_3 2})

x = \\frac{1}{𝑙𝑜𝑔_2 5}) / \\frac{1}{𝑙𝑜𝑔_2 3}) = \\frac{log_2 3}{𝑙𝑜𝑔_2 5}) = log_{5}(3)

Going through the options, Simplifying (B)

1 + log_{5} (\\frac{3}{5}))

1 + log_{5}(3) - log_{5}(5)

1 + log_{5}(3) – 1

log_{5}(3)

The question is **" If x is a positive quantity such that 2 ^{x} = 3^{log52} , then x is equal to " **

Choice B is the correct answer.

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