Question

Find the value of x: 25^x-1 + 100 = 5^2x/5

Answer 1

Answer:

$\displaystyle{x = 2}$

Step-by-step explanation:

$\displaystyle{25^{x-1}+100=\dfrac{5^{2x}}{5} }\\\\\\\displaystyle{5^{2x-2}+100=\dfrac{5^{2x}}{5} }\\\\\\\displaystyle{\dfrac{5^{2x}}{25} +100=\dfrac{5^{2x}}{5} }\\\\\\\displaystyle{ \text{Let }{5^{2x} = y}}$

$\displaystyle{\dfrac{y}{25} +100 = \dfrac{y}{5}}\\\\\\\displaystyle{\dfrac{y}{25} -\dfrac{y}{5} }=-100}\\\\\\\displaystyle{\dfrac{ - 4 y}{25} =-100}\\\\\\\displaystyle{y = 25^{2}}$

$\displaystyle{\text{Now putting value of y}}\\\\\\\displaystyle{5^{2x}=25^{2}}\\\\\\\displaystyle{5^{2x}=5^{2\times2}}\\\\\\\displaystyle{x=2}$

$\displaystyle{\text{Hence, the value of x is 2.}}$