Chapter 5: Q 57. (page 298)

Find $a$ so that the graph of $f (x) = \log_{a} x$ contains the point $(2, 2)$

Short Answer

Expert verified

The value of $' a'$ is $\sqrt{2}$

Step by step solution

Step 1. Given information

Given function is $y = \log_{a} x$

Step 2. Omitting logaritm

Omitting logarithm, we have,

$x = a^{y}$

Now, the function holds the point $(2, 2)$

Hence, putting the point to the function we have,

$2 = a^{2}$

By square rooting both sides, we have,

$a = \sqrt{2}$

Step 3. Check

Now, for $a = \sqrt{2}$ ,

we have,

$\log_{\sqrt{2}} 2 = \log_{\sqrt{2}} {(\sqrt{2})}^{2} = 2 \times \log_{\sqrt{2}} \sqrt{2} = 2 \times 1 = 2$

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Find $a$ so that the graph of $f (x) = \log_{a} x$ contains the point $(2, 2)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Omitting logaritm

Step 3. Check

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Find $a$ so that the graph of $f (x) = \log_{a} x$ contains the point $(2, 2)$