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.