Question

If 5 ^2x+1 ÷25= 125 find the value of x.​

Answer 1

Step-by-step explanation:

Given:-

5^(2x+1)÷25 = 125

To find:-

Find the value of x?

Solution:-

Given that

5^(2x+1)÷25 = 125

=> 5^(2x+1)÷5^2 = 5^3

=> 5^(2x+1) / 5^2 = 5^3

We know that

a^m / a^n = a^(m-n)

Where a = 5 and m = 2x+1 and n = 2

=> 5^(2x+1-2) = 5^3

=>5^(2x-1) = 5^3

Since the bases are equal then exponents must be equal.

=> 2x-1 = 3

=>2x = 3+1

=>2x = 4

=>x = 4/2

=>x = 2

Answer:-

The value of x for the given problem is 2

Check:-

If x = 2 then LHS

5^(2x+1)÷25

= 5^(2×2+1)÷25

=5^(4+1)÷25

=> 5^5÷25

=>5^5÷5^2

=> 5^(5-2)

=>5^3

=>5×5×5

=125

=RHS

LHS = RHS is true for x=2

Used formula:-

• a^m / a^n = a^(m-n)