Question

Find the value of x , if 3^4*3^5= (3^3)^x​

Answer 1

Answer:

Answer

By trial, x=2 is a root of the equation . Dividing the equation by 5

x

we get

(

5

3

)

x

+(

5

4

)

x

=1

If x<2, then (3/5)

x

>(3/5)

2

and (4/5)

x

>(4/5)

2

and so on

(3/5)

x

+(4/5)

x

>(3/5)

2

+(4/5)

2

=1

Hence (1) is not satisfied for any value of x<2.

Similarly, for x>2, we will always have the inequality (3/5)

x

+(4/5)

x

<1

Thus x=2 is the only root of the given equation. Note that it is immaterial how we found a root, but it is necessary to show that there are no other roots.

Answer 2

$\huge\underline\mathfrak\blue{\:♡Solution\:♡}$

Answer :

Given,

3⁴ × 3⁵ = (3³)ˣ

⇒ 3⁴⁺⁵ = (3³)ˣ

⇒ 3⁹ = (3³)ˣ

⇒ (3³)³ = (3³)ˣ

Comparing both sides, we get x = 3

∴ The required value of x is 3