Solve for all real values of x is 9^x+2=240+9^x
THIS ONE IS HARD
It won't seem hard after you've done a few dozen of them...
I assume you meant
9^(x+2)=240+9^x
That is the same as
9^2*9^x = 240 + 9^x
9^x(81-1) = 240
80*9^x = 240
9^x = 3
x = 1/2
To solve the equation 9^(x+2) = 240 + 9^x for all real values of x, we can start by simplifying both sides of the equation.
Let's first simplify the right side of the equation by combining like terms: 240 + 9^x.
Now, let's rewrite both sides with a common base. Since both sides have 9 as their base, we can rewrite the equation as follows:
9^(x+2) = 9^4 + 9^x
Now that the bases are the same, we can equate the exponents on both sides:
x + 2 = 4 + x
By subtracting x from both sides, we get:
2 = 4
However, we have reached a contradiction since 2 is not equal to 4. This means that there are no real solutions for this equation.
In conclusion, there are no real values of x that satisfy the equation 9^(x+2) = 240 + 9^x.