NakafaLearn free and with quality.

Nakafa School

Subject

- Bachelor

Exercises

- TKA
- SNBT

Holy

Quran

Articles

Politics

Community
About

Command Palette

Search for a command to run...

Question 20

Number 20

If $x_1$ and $x_2$ satisfy the equation $(2 \log x - 1) \cdot \frac{1}{\log_x 10} = \log 10$ , then $x_1x_2 = ....$

$5\sqrt{10}$

$4\sqrt{10}$

$3\sqrt{10}$

$2\sqrt{10}$

$\sqrt{10}$

Explanation

Let $p = \log_{10} x = \log x$ , then

(2 \log x - 1) \cdot \frac{1}{\log_x 10} = \log 10

(2 \log_{10} x - 1) \cdot \log_{10} x = 1

(2p - 1)p = 1

2p^2 - p - 1 = 0

(2p + 1)(p - 1) = 0

p = -\frac{1}{2} \cup p = 1

Determining the value of $x$ from $p$

p = -\frac{1}{2} \rightarrow \log_{10} x = -\frac{1}{2} \rightarrow x_1 = 10^{-\frac{1}{2}}

p = 1 \rightarrow \log_{10} x = 1 \rightarrow x_2 = 10

So the product of $x_1x_2$

10^{-\frac{1}{2}} \cdot 10 = 10^{\frac{1}{2}} = \sqrt{10}

Comments

Question 20Set 3

Exercises

Number 20

Report