Lets trancend your indices skill

Probability Level 2

2 x = 3 y = 6 z 2^x = 3^y = 6^z

Express z z in terms of x x and y . y.

x y = z xy = z 1 / x + 1 / y = 1 / z 1/x+1/y=1/z y x = z \frac{y}{x} = z None of the above

Thevarraaj Chandran by Thevarraaj Chandran , 22, Malaysia

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2 solutions

Karan Gujar
Sep 7, 2014

Such simple problems are fr 6th&7th grade students,i m mot finding something complex in this app!! Plz ask sumthing tough

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Let a be 2^x. Then therotically a is equal to 3 and 6. Shift x to the other side and it becomes a reciprocal. Simple math2×3is 6. Then reciprocal x multiplied by reciprocal y isreciprocal z. Then, solve the equation and express z!!!!.

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The correct answer is 1 / x + 1 / y = 1 / z 1/x + 1/y = 1/z .

Taking the logarithm of both sides of 2 x = 6 z 2^x = 6^z , we get log ⁡ 2 x = log ⁡ 6 z \log 2^x = \log 6^z . Then x log ⁡ 2 = z log ⁡ 6 x \log 2 = z \log 6 , so x = z log ⁡ 6 log ⁡ 2 . x = \frac{z \log 6}{\log 2}. Similarly, y = z log ⁡ 6 log ⁡ 3 . y = \frac{z \log 6}{\log 3}. Then 1 x + 1 y = log ⁡ 2 z log ⁡ 6 + log ⁡ 3 z log ⁡ 6 = log ⁡ 6 z log ⁡ 6 = 1 z . \frac{1}{x} + \frac{1}{y} = \frac{\log 2}{z \log 6} + \frac{\log 3}{z \log 6} = \frac{\log 6}{z \log 6} = \frac{1}{z}.

Jon Haussmann - 6 years, 9 months ago

@Thevarraaj Chandran I do not understand what you are trying to say. I agree that the answer should be 1 / x + 1 / y = 1 / z 1/x + 1/y = 1/z , and will update the problem accordingly.

Calvin Lin Staff - 6 years, 9 months ago

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