1.find x and y if 3 raise to the power 2x-y equals 1 and 16 raise to the power x divided by 4 equals 8 raise to the power 3x-y
2. solve 2x-3y 2=x 2y-5=3x y?
3^(2x-y)=1
log base three, both sides, gives...
2x-y=0
and 16^(x/4)=8^(3x-y)
take log base 2 of each side
4(x/4)=3(3x-y)
x=9x-3y
8x-3y=0 and with
2x-y=0 solve.
good luck with that.
I suspect a typo -- an ambiguity in the words.
poppy, fix the equations and you can arrive at a solution.
To find the values of x and y in the given equations, we will solve them step by step.
1. Equation 1: 3^(2x - y) = 1
To solve this equation, we can rewrite 1 as a power of 3:
3^0 = 1
Comparing the powers on both sides, we get:
2x - y = 0 [Equation A]
2. Equation 2: (16^x)/4 = 8^(3x - y)
We know that 16 is the same as 4^2, and 8 is the same as 2^3. Substituting these values, we get:
[(4^2)^x] / 4 = (2^3)^(3x-y)
4^(2x) / 4 = 2^(3(3x-y))
4^(2x) / 4 = 2^(9x - 3y)
We can rewrite 4 as a power of 2:
(2^2)^(2x) / 4 = 2^(9x - 3y)
Using the exponent properties, we can simplify the equation:
2^(4x) / 4 = 2^(9x - 3y)
By equating the powers of 2, we get:
4x = 9x - 3y [Equation B]
Now, we have two equations A and B. Let's solve them simultaneously to find the values of x and y.
Equation A: 2x - y = 0
Equation B: 4x = 9x - 3y
Rearrange Equation B to solve for y:
9x - 4x = 3y
5x = 3y
Substitute this value of y into Equation A:
2x - (5x/3) = 0
Multiply through by 3:
6x - 5x = 0
Simplifying the equation, we get:
x = 0
Substitute the value of x back into Equation A to find y:
2(0) - y = 0
- y = 0
y = 0
Therefore, the solution to the system of equations is:
x = 0
y = 0
2. Equation 1: 2x - 3y = 2
Equation 2: x = 2y - 5
To solve this system of equations, we can substitute the value of x from Equation 2 into Equation 1.
Substituting x = 2y - 5 into Equation 1, we get:
2(2y - 5) - 3y = 2
Simplifying the equation, we get:
4y - 10 - 3y = 2
y - 10 = 2
y = 2 + 10
y = 12
Substitute the value of y back into Equation 2 to find x:
x = 2(12) - 5
x = 24 - 5
x = 19
Therefore, the solution to the system of equations is:
x = 19
y = 12