Question

What is Log a base b× log b base c× log c base a?

Answer 1

Hope it will help you

Answer 2

The Answer is 1.


Here we are going to use just one simple concept:

$\boxed{\log_{y} x = \frac{\log_z x}{\log_z y}}$

Where z is any suitable base we like.


Here we will use z = 10, so as to simplify the question as a common logarithm.

$LHS \\ \\ \\ = \log_b a \times \log_c b \times \log_a c \\ \\ \\ = \frac{\log a}{\log b} \times \frac{\log b}{\log c} \times \frac{\log c}{\log a} \\ \\ \\ = 1 \\ \\ \\ = RHS$

$\mathbb{H}\mathfrac{ence} \, \, \mathbb{P}\mathfrac{roved}$