3^x-2 = 9^x+4
I hope you mean
3^(x-2) = 9^(x+4) since my solution will assume that
realize that 9 = 3^2
so 3^(x-2) = 9^(x+4) is
3^(x-2) = 3^(2x+8)
then
2x+8 = x-2
x = -10
check:
LS = 3^-12 = .000001881
RS = 9^-6 = .000001881
how did you get 3^(2x+8)
9^(x+4)
= (3^2)^(x+4)
= 3^(2x+8)
just like (x^a)^b = x^(ab)
To solve the equation 3^x-2 = 9^x+4, we need to isolate the variable x. Here's how:
First, let's simplify the equation by expressing both sides with the same base.
Since 9 can be written as 3^2, we can rewrite 9^x+4 as (3^2)^(x+4).
Using the property of exponents, we can multiply the exponents when raising a power to another power: (a^m)^n = a^(m*n).
So, (3^2)^(x+4) becomes 3^(2*(x+4)) = (3^(x+4))^2.
Now, our equation becomes 3^x-2 = (3^(x+4))^2.
Next, let's simplify the equation further.
We can rewrite 3^(2*(x+4)) as 3^(2x+8).
Now, our equation simplifies to 3^x-2 = (3^(x+4))^2 = 3^(2x+8).
To eliminate the exponents, we can take the logarithm of both sides of the equation. Let's take the base 3 logarithm:
log base 3 (3^x-2) = log base 3 (3^(2x+8)).
Using the logarithmic property, log base a (a^b) = b, the equation becomes:
x - 2 = 2x + 8.
Now, let's solve for x.
Subtract x from both sides:
x - 2x = 8 + 2.
Simplifying further, we get:
-x = 10.
Multiplying both sides by -1, we have:
x = -10.
Therefore, the solution to the equation 3^x-2 = 9^x+4 is x = -10.