7 raise to power 2x -2(7 raise to power x) +1=0.

Answer 1

To solve the equation 7^(2x) - 2(7^x) + 1 = 0, let's make a substitution:

Let u = 7^x.

Substituting this into the equation, we get u^2 - 2u + 1 = 0.

Now we can solve this quadratic equation:

(u - 1)(u - 1) = 0

(u - 1)^2 = 0

Taking the square root of both sides, we have:

u - 1 = 0

u = 1

Substituting back u = 7^x, we have:

7^x = 1

Since any number raised to the power of 0 is equal to 1, we have:

x = 0