Question

4^x=7^y=28 then x+y/xy​

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Answer 1

Answer:

$02 \sqrt[0 \times \frac{?}{?} ]{?} \times \frac{?}{?}$

Answer 2

Given,

$\[{4^x} = {7^y} = 28\]$

$\[\frac{{x + y}}{{xy}} = ?\]$

Solution,

$\[\begin{array}{l}{4^x} = 28\\ \Rightarrow x\ln 4 = \ln 28\\ \Rightarrow \frac{1}{x} = \frac{{\ln 4}}{{\ln 28}}\end{array}\]$--------(1)

$\[\begin{array}{l}{7^y} = 28\\ \Rightarrow y\ln 7 = \ln 28\\ \Rightarrow \frac{1}{y} = \frac{{\ln 7}}{{\ln 28}}\end{array}\]$--------(2)

Calculate the value,

$\[\begin{array}{l} = \frac{{x + y}}{{xy}}\\ = \frac{1}{y} + \frac{1}{x}\end{array}\]$

Put the values from equation 1 and 2,

$\[\begin{array}{l} = \frac{{\ln 7}}{{\ln 28}} + \frac{{\ln 4}}{{\ln 28}}\\ = \frac{1}{{\ln 28}}\left( {\ln 7 + \ln 4} \right)\\ = \frac{1}{{\ln 28}}\left( {\ln \left( {7 \times 4} \right)} \right)\\ = \frac{1}{{\ln 28}} \times {\mathop{\rm l}\nolimits} \end{array}\]$

Hence the value of expression is 1.