Question

If 3^x = 5^y = 75^z, show that z= ( xy ) / ( 2x + y )

Answer 1

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If 3^x=5^y=75^z show that z=xy/(2x+y)?
1 answer · Mathematics
Answer
i) Let 3^x = 5^y = 75^z = k

ii) So, 3 = k^(1/x); 5 = k^(1/y) and 75 = k^(1/z)

iii) 75 = 3 x 25 = 3 x 5²
Substituting the values from step (ii) above,
k^(1/z) = {k^(1/x)}*{k^(2/y)} = k^(1/x + 2/y) [By the law of exponents]

Equating the powers from both sides,
1/z = 1/x + 2/y = (y + 2x)/xy

Taking reciprocal, z = (x*y)/(2x + y) [Proved]

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