(10^2t)-2(10^t)+1=0
let 10^t=y
please help
Sure! Let's solve the equation (10^2t) - 2(10^t) + 1 = 0 by substituting 10^t with y.
Given equation: (10^2t) - 2(10^t) + 1 = 0
Now, substitute 10^t with y:
y^2 - 2y + 1 = 0
This is a quadratic equation in terms of y. We can solve it using factoring, completing the square, or the quadratic formula. Let's use factoring in this case.
The equation (y^2 - 2y + 1 = 0) can be factored into:
(y - 1)^2 = 0
To solve this equation, we set (y - 1)^2 = 0 and solve for y. Taking the square root of both sides, we find:
y - 1 = 0
y = 1
Now, substitute back y = 10^t into the equation to find the value of t:
10^t = 1
10 raised to any power (except for 0) is always greater than 1. Therefore, the only solution is when t equals 0:
t = 0
So, the solution to the equation (10^2t) - 2(10^t) + 1 = 0 is t = 0.