Question

solve for x
5²x+1=3x625 ​

Answer 1

5^2x +1=5^3× 5^4

2x+1=3×4

2x=12-1

x=11/2

x=5.5

Answer 2

Given,

$5^{2x+1} =5^{3} \times625$

From above $625$ can be written as $5^{4}$

$5^{2x+1} =5^{3} \times 5^{4}$

In $5^{3} \times5^{4}$, the bases are equal the powers should be added.

$a^{m}\times a^{n} =a^{m+n}$

We get,

$5^{2x+1} =5^{3+4}$

$5^{2x+1} =5^{7}$

As we know the bases are equal powers should be equated.

We get

$2x+1=7$

$2x=7-1$

$2x=6$

$x=3$

Therefore, the value of $x$ is $3$