Question

if 5 raise to the power 2x +1 × 25 = 125. find the value of x​

Answer 1

Solution :

↪5^ 2x + 1 × 25 = 125

↪5^2x+1 × 5² = 5³

↪5^2x+1 + 2 = 5³

↪5^2x+3 = 5³

↪2x + 3 = 3

↪2x = 3 - 3

↪2x = 0

•°• x = 0

Therefore, Required Value of x is 0.

Answer 2

${5}^{2x + 1}\times 25 = 125$

We know that

25 = 5^2

and 125 = 5^3

$\implies{5}^{2x + 1}\times{5}^{2} ={5}^{3}$

We know the identity a^x × a^y = a^(x+y )

$\implies{5}^{2x + 1 + 2}={5}^{3}$

$\implies \:{5}^{2x + 3}={5}^{3}$

Now, the bases are same, so comparing the exponents

2x+3 =3

2x=3-3

2x=0

x=0/2

x=0

__________________________

Verification

${5}^{2x + 1}\times 25$

$={5}^{2 \times 0 + 1}\times 25$

$={5}^{0 + 1}\times 25$

$={5}^{1}\times 25$

$= 5\times 25$

$= 125$

= RHS

Hence verified