Question

23. If (3) x= (5) y=(75)z , then prove that z = /2+

Answer 1

Step-by-step explanation:

Let 3^{x}=5^{y}=75^{z}= M3

x

=5

y

=75

z

=M , then

3= M^{\frac{1}{x}}3=M

x

1

, 5= M^{\frac{1}{y}}5=M

y

1

and 75= M^{\frac{1}{z}}75=M

z

1

.

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

2

×3

M^{\frac{1}{z}}= M^{\frac{2}{y}}{\times}M^{\frac{1}{x}}M

z

1

=M

y

2

×M

x

1

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

z

1

=M

y

2

+

x

1

\frac{1}{z}=\frac{2}{y}+\frac{1}{x}

z

1

=

y

2

+

x

1

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

z

xy

=2x+y

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

2+y

xy

Hence proved.

Answer 2

Step-by-step explanation:

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