Question

What is the value of x that makes the equation true? 2\−5⋅2\x=2\10

Answer 1

Correct option is

A

2

 log(2x) is valid when x>0

log5(2x2+3x+2)41=log25(2x)

$$\Rightarrow \dfrac{1}{4}\log _{ 5 }{ { \left( { 2x }^{ 2 }+3x+2 \right)  } } =\dfrac{1}{2}\log _{ 5 }{ (2x) }  \quad [\because \log a^m=m\log a  \text&  \log_{a^m}b=\dfrac{1}{m}\log_ab]$$

⇒log5(2x2+3x+2)=log5(2x)2

⇒2x2+3x+2=(2x)2

⇒−2x2+3x+2=0⇒x=2asx>0

Answer 2

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$\frac{2}{ - 5} \times \frac{2}{x} = \frac{2}{10} \\ x = \frac{4 \times 10}{ - 5 \times 2} \\ x = - 4$

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