Question

Q12. Which of the following is true. If 1/ab +1/bc +1/ac = 1/abc

al) log(ab + bc + ca) = abc
b) log (1/a + 1/b + 1/c) = abc
c) log(abc) = 0
d) log(a + b + c) = 0​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ac} = \frac{1}{abc} }$

a) log(ab + bc + ca) = abc

b) log (1/a + 1/b + 1/c) = abc

c) log(abc) = 0

d) log(a + b + c) = 0

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ac} = \frac{1}{abc} }$

We now simplify it as below

$\displaystyle \sf{ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ac} = \frac{1}{abc} }$

$\displaystyle \sf{ \implies\frac{c + a + b}{abc} = \frac{1}{abc} }$

$\displaystyle \sf{ \implies\frac{a + b + c}{abc} = \frac{1}{abc} }$

$\displaystyle \sf{ \implies \: a + b + c = 1 }$

Taking logarithm in both sides we get

$\displaystyle \sf{ \log(\: a + b + c )= \log 1 }$

$\displaystyle \sf{ \implies \log(\: a + b + c )= 0 }$

FINAL ANSWER

The correct option is

$\displaystyle \sf{ d) \: \: \log(\: a + b + c )= 0 }$

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