Question

solution of the equation 5^2x-5^x+3+125=5^x is

Answer 1

solution of the equation 5^2x-5^x+3+125=5^x is

5^2x-5^(x+3)+125=5^x  

let suppose,

5^x=b

5^2x=b^2

b^2-125b+125=b

b^2-126b+125=0

b=125,1

so that, 5^(x)=125 = 5^(3 )or 5^(x)=1 = 5^0

so here it is  x=3 / x=0

Answer 2

Answer:

Step-by-step explanation:

5^(2x) - 5^(x + 3) + 125 = 5^(x)

5^(2x) - 5^3 * 5^(x) + 125 = 5^x

5^(2x) - 125 * 5^(x) - 5^(x) + 125 = 0

5^(2x) - 126 * 5^(x) + 125 = 0

5^(x) = (126 +/- sqrt(126^2 - 4 * 1 * 125)) / (2 * 1)

5^(x) = (126 +/- sqrt(15876 - 500)) / 2

5^(x) = (126 +/- 124) / 2

5^(x) = 250/2 , 2/2

5^(x) = 125 , 1

x * ln(5) = ln(125) , ln(1)

x * ln(5) = ln(5^3) , 0

x * ln(5) = 3 * ln(5) , 0

x = 3 * ln(5) / ln(5) , 0 / ln(5)

x = 3 , 0

Hope it helps!