If 52x+1 /25 = 125, find the value of x - Maths - Exponents and Powers

Question

If 5 2x+1
/25 = 125, find the value of x

Aakash Sharma · Accepted Answer

$\frac{5^{2 x + 1}}{25} = 125 \Rightarrow \frac{5^{2 x + 1}}{5^{2}} = 5^{3} \Rightarrow 5^{2 x + 1 - 2} = 5^{3} \Rightarrow 5^{2 x - 1} = 5^{3}$

Comparing the indices of 5 we get

$2 x - 1 = 3 \Rightarrow 2 x = 3 + 1 = 4 \Rightarrow x = \frac{4}{2} = 2$

If 5 2x+1 /25 = 125, find the value of x.