Question

step by step soln plz​

Answer 1

Answer:

Explanation :

Solution

(2x)ln2=(3y)ln3

Taking ln both sides,

⇒(ln2)(ln2x)=(ln3)(ln3y)

⇒(ln2)(ln2+lnx)=(ln3)(ln3+lny)→(1)

Now, we will take the second equation,

3lnx=2lny

Taking ln both sides,

⇒(lnx)(ln3)=(lny)(ln2)

⇒(lny)=(lnx)(ln3)ln2

Putting value of lny in (1),

(ln2)(ln2+lnx)=(ln3)(ln3+(lnx)(ln3)ln2)

⇒(lnx)(ln2−((ln3)2ln2))=(ln3)2−(ln2)2

⇒lnxln2((ln2)2−(ln3)2)=(ln3)2−(ln2)2

⇒lnxln2=−1

⇒(lnx)=ln(2)−1

⇒x=2−1⇒x=12, which is the required value of x0.