Question

.Find the value of x if (2/5) =(5/2)power 4 x (2/5)power x​

Answer 1

Answer:

log(2x) is valid when x>0

log

5

(2x

2

+3x+2)

4

1

=log

25

(2x)

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

⇒log

5

(2x

2

+3x+2)=log

5

(2x)

2

⇒2x

2

+3x+2=(2x)

2

⇒−2x

2

+3x+2=0⇒x=2asx>0

Ans: 2

Step-by-step explanation:

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