First slide

Introduction to real valued functions

Question

If $a^{x} = b, b^{y} = c, c^{z} = a,$ then value of $xyz$ is

Easy

A

0
B

1
C

2
D

3

Solution

$a^{x} + b \Rightarrow x \log a = \log b$
$\Rightarrow x = \frac{\log b}{\log a} = \log_{a} b$
Similarly $y = \log_{b} c, z = \log_{c} a$
$∴ xyz = \log_{a} b . \log_{b} c . \log_{c} a = 1 .$

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