solve the equation for x using the fact that if a^u =a^v then u=v. 9^-x+15=27x.
thanks
You must have a typo
If you want me to use the stated property, then you must have meant
9^(-x+15) = 27^x
if as assumed, then
(3^2)^(-x+15) = (3^3)^x
3^(-2x + 30) = 3^3x
-2x + 30 = 3x , using your stated property
-5x = -30
x = 6
thanks
To solve the equation 9^(-x+15) = 27x using the given fact, we will first simplify the equation and then use the fact to equate the exponents.
Step 1: Simplify the equation
Using the property (a^m)^n = a^(m*n), we can rewrite 9^(-x+15) as (9^(-1))^x * 9^15. This simplifies to (1/9)^x * 9^15 = 27x.
Step 2: Equate the exponents
According to the given fact, if (a^u) = (a^v), then u = v. We can apply this fact to the exponents of the bases 1/9 and 9.
Setting the exponents equal, we have x = 15 + 27x.
Step 3: Solve for x
To solve for x, we will isolate the variable on one side of the equation:
x - 27x = 15,
-26x = 15,
x = 15 / (-26),
x = -15/26.
Therefore, the solution to the equation 9^(-x+15) = 27x using the given fact is x = -15/26.