Logarithm - Arithmetic Aptitude Questions and Answers

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Add the equation x = 1 + log_a bc, y = 1 + log_b ca and z = 1 + log_c ab. Find the value of Apti Logarithm

xyz = xy + yz + zx

X²yz = xyz + yx + 1

(xz + 1)² = xy - yz - zx

(xz + y) = xy + yz + zx

Answer : Option A

Explanation :

x =1 + log_a bc

We can write it as x = log_a a + log_a bc => log_a abc

Similarly, y = log_b b + log_b ca => log_b abc

And, z = log_c c + log_c ab => log_c abc
Changing the values of x, y, z to a common base m by using log_b a =, we get
X =

Y =

Z =

Now, =[log_m a + log_m b + log_m c]

Now, Right hand side equation, [log_m abc/ log_m abc] = 1
Now, = 1

Or, = 1 => xyz =xy + yz + zx.

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