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Try yourself:Let x and y be positive real numbers such that log_{5}(x + y) + log_{5}(x - y) = 3, and log_{2}y - log_{2}x = 1 - log_{2}3. Then xy equals

[2019]

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Try yourself:If x is a real number ,then is a real number if and only if

[2019]

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Try yourself:The real root of the equation 2^{6x} + 2^{3x+2 }- 21 = 0 is

[2019]

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

[2018]

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Try yourself:If log_{2}(5 + log_{3}a) = 3 and log_{5}(4a + 12 + log_{2}b) = 3, then a + b is equal to

[2018]

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Try yourself:If log_{12}81 = p, then is equal to:

[2018]

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Try yourself:If p^{3} = q^{4 }= r^{5} = s^{6}, then the value of logs (pqr) is equal to

[2018]

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Try yourself:

[2018]

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Try yourself:Suppose, log_{3}x = log_{12}y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log_{6}G is equal to:

[2017]

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Try yourself:If 9^{2x – 1} – 81^{x-1} = 1944, then x is

[2017]

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Try yourself:If x is a real number such that log_{3}5 = log_{5}(2 + x), then which of the following is true?

[2017]

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*Answer can only contain numeric values

Try yourself:If log(2^{a} × 3^{b} × 5^{c}) is the arithmetic mean of log(2^{2} × 3^{3} × 5), log(2^{6} × 3 × 5^{7}), and log(2 × 3^{2} × 5^{4}), then a equals

[TITA 2017]

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Try yourself:The value of log_{0.008}√5 + log_{√3}81 – 7 is equal to:

[2017]

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Try yourself:If 9^{x - (1/2)} – 2^{2x – 2} = 4^{x} – 3^{2x – 3}, then x is

[2017]

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