Question

if 2 by 5 whole power x is equal to 5 by 2 whole power x into 4 by 25 then find x ​

Answer 1

Answer:

the value of X=1

Take the 5/2 whole power x toward the R.H.S by reciprocating and then in L.H.S there will be only 4/25 whole power 1 then multiply the R.H.S you will get the answer as 4/25 the whole x then using the identity you will get the answer as 1.

Answer 2

Given: $(\dfrac{2}{5} )^x=(\dfrac{5}{2} )^x\times \dfrac{4}{25}$

To find: The value of x

Step-by-step explanation:

Now as given we have

$(\dfrac{2^x}{5^x} )=(\dfrac{5^x}{2^x} )\times \dfrac{4}{25} \text { } [\because (\dfrac{a}{b} )^n=\dfrac{a^n}{b^n} ]\\\\\Rightarrow \dfrac{2^x \times 2^x}{5^x \times 5^x} =(\dfrac{2}{5})^2\\\\\Rightarrow \dfrac{2^{2x}}{5^{2x}} =(\dfrac{2}{5})^2 \text { } [\because a^n+a^m=a^{m+n}]\\\\\Rightarrow( \dfrac{2}{5} )^{2x}=(\dfrac{2}{5})^2$

Now comparing the exponents and powers we get

$2x=2\\\\\Rightarrow x=1$

Hence , the value of x is 1