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Chapter 5: Q 106. (page 309)

If $f (x) = \log_{a} x$ , show that $f (A B) = f (A) + f (B)$ .

Short Answer

Expert verified

The result is shown in the explanation.

Step by step solution

01

Step 1. Given information.

Consider the given function.

$f (x) = \log_{a} x$

02

Step 2. Calculation.

Substitute AB for x in the given function.

$\begin{array}{rcl} f (A B) & = & \log_{a} (A B) \\ = & \log_{a} A + \log_{a} B \\ = & f (A) + f (B) \end{array}$

Since the left side is equal to the right side.
The given equation has been proved.

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