Question

If 2^x=10^y=50^z. Then show that y= 2xy/z+x

Answer 1

Answer:

Answer:

Step-by-step explanation:

Let 3^{x}=5^{y}=75^{z}= M3x=5y=75z=M , then

3= M^{\frac{1}{x}}3=Mx1 , 5= M^{\frac{1}{y}}5=My1 and 75= M^{\frac{1}{z}}75=Mz1 .

Also, 75 can be written as: 75=5^{2}{\times}375=52×3

M^{\frac{1}{z}}= M^{\frac{2}{y}}{\times}M^{\frac{1}{x}}Mz1=My2×Mx1

M^{\frac{1}{z}}=M^{\frac{2}{y}+\frac{1}{x}}Mz1=My2+x1

\frac{1}{z}=\frac{2}{y}+\frac{1}{x}z1=y2+x1

\frac{xy}{z}=2x+yzxy=2x+y

z=\frac{xy}{2+y}z=2+yxy

Hence proved.

Step-by-step explanation:

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