Math, asked by AyushTewari, 1 year ago

if 3^x = 5^y = 75^z show that z =xy/2x+y

Answers

Answered by abhi178
4
Given, 3^x = 5^y = 75^z
Let 3^x = 5^y = 75^y = K
So, 3^x = K
Taking log both sides,
xlog3 = logK
x = logK/log3 ------(1)

Similarly, y = logK/log5--------(2)
and z = logK/log75

Now, z = logK/log75
= logK/log(5² × 3)
= LogK/[2log5 + log3]
From equations (1) and (2),
z = logK/[2logK/y + logK/x ]
= logK/logK[2/y + 1/x ]
= xy/(2x + y)

Hence, z = xy/(2x + y)

natasha41: the way u explained :heart_eyes: osum like u abhi bhai
Answered by sashigoku
0

Answer:

Step-by-step explanation:

given, 3^x = 5^y = 75^z

Let 3^x = 5^y = 75^y = K

So, 3^x = K

Taking log both sides,

xlog3 = logK

x = logK/log3 ------(1)

Similarly, y = logK/log5--------(2)

and z = logK/log75

Now, z = logK/log75

= logK/log(5² × 3)

= LogK/[2log5 + log3]

From equations (1) and (2),

z = logK/[2logK/y + logK/x ]

= logK/logK[2/y + 1/x ]

= xy/(2x + y)

Hence, z = xy/(2x + y)

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