Question

3^x-9*3^-x=8 Help me !

Answer 1

5895655786568755688679568

Answer 2

To solve the equation 3^x - 9 * 3^(-x) = 8, we can make use of a substitution to simplify the equation. Let's substitute y = 3^x:

Substituting y into the equation gives us y - 9/y = 8.

Multiplying both sides of the equation by y, we get y^2 - 9 = 8y.

Rearranging the equation, we have y^2 - 8y - 9 = 0.

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation gives (y - 9)(y + 1) = 0.

Setting each factor equal to zero, we have two possibilities:

1. y - 9 = 0, which implies y = 9.
2. y + 1 = 0, which implies y = -1.

Since y = 3^x, we can substitute these values back in to solve for x:

1. If y = 9, then 3^x = 9. Taking the logarithm of both sides, we have x * log(3) = log(9). Solving for x gives x = log(9) / log(3).
2. If y = -1, then 3^x = -1. However, there is no real value of x that satisfies this equation.

Therefore, the solution to the equation 3^x - 9 * 3^(-x) = 8 is x = log(9) / log(3).