Question

5^3x+1 = 5^2x-5 Find x​

Answer 1

Given

We have given 5^3x+1= 5^2x-5

To find

We have to find the value of x

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

➙5³ˣ⁺¹=5²ˣ⁻⁵

We see that 5 lies on both sides so,it gets automatically cancelled.

➙3x+1= 2x-5

Making Variable and constant terms together

➙3x-2x= -5-1

➙x= -6

Check:

➙5³ˣ⁺¹=5²ˣ⁻⁵

➙3x+1=2x-5

Taking LHS

➙3(-6)+1

➙-18+1

=-17

Taking RHS

➙2x-5

➙2(-6)-5

➙-12-5

= -17

Since,LHS = RHS(Verified)

Extra concepts

• If bases are same then powers gets added in multiplication and gets substracted in division.

=>aᵐ×aⁿ= a ᵐ⁺ⁿ

=>aᵐ÷ aⁿ= a ᵐ-ⁿ

• If power is 0 then it would be consider as 1

=>a⁰= 1

• Two unlike terms or value having same power then the values become whole to the power of:

=>aᵐ×bᵐ= (ab)ᵐ

=>aᵐ÷bᵐ= (a/b)ᵐ

Answer 2

Solution

➙5³ˣ⁺¹=5²ˣ⁻⁵

We see that 5 lies on both sides so,it gets automatically cancelled.

➙3x+1= 2x-5

Making Variable and constant terms together

➙3x-2x= -5-1

➙x= -6

Check:

➙5³ˣ⁺¹=5²ˣ⁻⁵

➙3x+1=2x-5

Taking LHS

➙3(-6)+1

➙-18+1

=-17

Taking RHS

➙2x-5

➙2(-6)-5

➙-12-5

= -17

Since,LHS = RHS(Verified)

Extra concepts

If bases are same then powers gets added in multiplication and gets substracted in division.

=>aᵐ×aⁿ= a ᵐ⁺ⁿ

=>aᵐ÷ aⁿ= a ᵐ-ⁿ

If power is 0 then it would be consider as 1

=>a⁰= 1

Two unlike terms or value having same power then the values become whole to the power of:

=>aᵐ×bᵐ= (ab)ᵐ

=>aᵐ÷bᵐ= (a/b)ᵐ