3^2x - 6 x 3^x + 9 = 0

Solve for x

I have no Idea what to do

sorry, the x in between 6 and three is multiplication... so it should be

3^2x - 6(3^x) + 9 = 0

I am going to rewrite the equation for you

(3x)2 - 6(3x) + 9 = 0

there is a strong hint there.

ahhh its a perfect square trinomial

(3^x - 3)^2 = 0

so x = 1

Glad you got it!

To solve the equation 3^(2x) - 6x * 3^x + 9 = 0 for x, we can use a technique known as substitution. This involves substituting a variable for a term in the equation to simplify it and make it easier to solve.

Let's start by making a substitution: let y = 3^x.

Now, we can rewrite the equation as follows:

y^2 - 6xy + 9 = 0

Notice that this is a quadratic equation in terms of y. We can solve it by factoring or using the quadratic formula. In this case, factoring seems to be a simpler option.

The equation can be factored as follows:

(y - 3)(y - 3) = 0

This simplifies to:

(y - 3)^2 = 0

Now, we can solve for y:

y - 3 = 0

y = 3

Remember, y is equal to 3^x, so we can substitute that back in:

3^x = 3

Now, we need to solve for x. Taking the logarithm (base 3) of both sides will help us isolate x.

log_3(3^x) = log_3(3)

x = 1

Therefore, the solution to the equation 3^(2x) - 6x * 3^x + 9 = 0 is x = 1.