Test Index

Logarithms

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Question : 30 of 85

Marks: +1, -0

If

\;\frac{\log x}{b-c} = \;\frac{\log y}{c-a} = \;\frac{\log z}{a-b},

then the value of

x y z

is:

1
0
2
none

Solution:

Concept:

Use the property that if

\frac{A}{B} = \frac{C}{D} = \frac{E}{F}

, then each ratio equals a common constant, say

k

.

Explanation:

Let

\frac{\log x}{b-c} = \frac{\log y}{c-a} = \frac{\log z}{a-b} = k

.

Then

\log x = k(b-c)

,

\log y = k(c-a)

,

\log z = k(a-b)

.

Add them:

\log x + \log y + \log z = k[(b-c)+(c-a)+(a-b)] = k(0) = 0

.

Hence

\log(xyz)=0

, so

xyz = 10^0 = 1

.

Answer:

1

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