Logx + logy=4 logx +2logy=3
logx+logy=4logx+2logy=3 ??? is the first equals sign a + ? If so, then
log(x*y*x^4*y^2=3
log (x^5 y^3)=3 and you can take the antilog
x^5y^3=1000
To solve the system of equations:
1. Start by subtracting the second equation from the first equation to eliminate the term "logx":
(logx + logy) - (logx + 2logy) = 4 - 3
logx - logx + logy - 2logy = 1
-logy = 1
2. Divide both sides of the equation by -1 to isolate "logy":
logy = -1
3. Substitute this value back into the second equation:
logx + 2(-1) = 3
logx - 2 = 3
logx = 5
4. Rewrite the equation using the exponential form:
x = 10^logx = 10^5 = 100,000
5. Therefore, the solution to the system of equations is x = 100,000 and y = -1.
To solve the system of equations:
1. Start by subtracting the second equation from the first equation to eliminate the "logx" term:
(logx + logy) - (logx + 2logy) = 4 - 3
Simplifying, you get:
-logy = 1
2. Divide both sides of the equation by -1 to isolate "logy" on one side:
logy = -1
3. Now substitute the value of "logy" (-1) back into either of the original equations (let's use the first equation for this example):
logx + logy = 4
logx + (-1) = 4
Simplifying:
logx - 1 = 4
4. Add 1 to both sides of the equation to isolate "logx":
logx = 4 + 1
logx = 5
5. Since the equations are given in logarithmic form, you can convert them to exponential form to find the actual values of x and y. Recall that the logarithmic form logx(y) = z is equivalent to the exponential form y = 10^z.
Hence, x = 10^5 (from logx = 5) and y = 10^(-1) (from logy = -1).
Therefore, the solution to the system of equations is x = 10^5 and y = 0.1.
from what you have:
Logx + logy=4 logx +2logy=3
log(xy) = log(x^4 y^2) = 3
so : log(xy) = log(x^4 y^2)
x^4 y^2 = xy
x^3 y = 1
y = 1/x^3 , of course x > 0
in logx + logy = 3
logx + log(1/x^3) = 3
log(x(1/x^3)) = 3
log (1/x^2) = 3
1/x^2 = 10^3 = 1000
1000x^2 = 1
x^2 = 1/1000
x = 1/10√10 = √10/100 or appr .03162
y = 1/x^3 = 10000√10 or appr 31622.8