Solve the following equation:\displaystyle\, \log^2 (100x) + \log^2\, (10x) = 14 + \log \frac{1}{x}

Name: Solve the following equation:\displaystyle\, \log^2 (100x) + \log^2\, (10x) = 14 + \log \frac{1}{x}
Uploaded: 2021-01-01T18:41:02.000Z
Duration: 2 min
Description: Solve the following equation:\displaystyle\, \log^2 (100x) + \log^2\, (10x) = 14 + \log \frac{1}{x}

lo g 2 ( 1 0 0 x ) + lo g 2 ( 1 0 x ) = 1 4 + lo g x 1 ⇒ ( 2 + lo g x ) 2 + ( 1 + lo g x ) 2 = 1 4 − lo g x ⇒ 2 ( lo g x ) 2 + 6 lo g x + 5 = 1 4 − lo g x ⇒ 2 ( lo g x ) 2 + 6 lo g x + 5 = 1 4 − lo g x ⇒ 2 ( lo g x ) 2 + 7 1 lo g x − 9 = 0 ⇒ 2 ( lo g x + 9 ) ( lo g x − 1 ) = 0 ⇒ lo g x = 2 − 9 , 1 ⇒ x = 1 0 2 − 9 , 1 0

Solve the following equation:\displaystyle\, \log^2 (100x) + \log^

Class 11 Math Algebra Logarithm and Antilogarithm

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Solve the following equation:

lo g^{2} (100 x) + lo g^{2} (10 x) = 14 + lo g \frac{1}{x}

Solution:

$lo g^{2} (100 x) + lo g^{2} (10 x) = 14 + lo g \frac{1}{x} \Rightarrow (2 + lo g x)^{2} + (1 + lo g x)^{2} = 14 - lo g x \Rightarrow 2 (lo g x)^{2} + 6 lo g x + 5 = 14 - lo g x \Rightarrow 2 (lo g x)^{2} + 6 lo g x + 5 = 14 - lo g x \Rightarrow 2 (lo g x)^{2} + 71 lo g x - 9 = 0 \Rightarrow 2 (lo g x + 9) (lo g x - 1) = 0 \Rightarrow lo g x = \frac{- 9}{2}, 1 \Rightarrow x = 1 0^{\frac{- 9}{2}}, 10$

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