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Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.?
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Log a to the base e whole dived by( y-z )= log b to the base e whole d...
Given Equation:
Log a to the base e / (y-z) = log b to the base e / (z-x) = log c to the base e / (x-y)
Finding the Value of a^(yz) * b^(zx) * c^(xy):
Let's solve the given equations one by one and then calculate the final expression.
Solving the Given Equations:
1. Log a / (y-z) = log b / (z-x)
Using the property of logarithms, we can rewrite the equation as:
a / (y-z) = b / (z-x)
This implies a = b * (y-z) / (z-x)
2. Log b / (z-x) = log c / (x-y)
Similarly, rewriting the equation gives:
b / (z-x) = c / (x-y)
This implies b = c * (z-x) / (x-y)
3. Substituting the value of b from equation 2 into equation 1:
a = (c * (z-x) / (x-y)) * (y-z) / (z-x)
= c * (y-z) / (x-y)
4. Now, we need to find a^(yz) * b^(zx) * c^(xy):
Substituting the values of a, b, and c into the expression:
a^(yz) * b^(zx) * c^(xy)
= (c * (y-z) / (x-y))^(yz) * (c * (z-x) / (x-y))^(zx) * c^(xy)
= c^(yz) * (y-z)^yz / (x-y)^yz * c^(zx) * (z-x)^zx / (x-y)^zx * c^(xy)
Final Expression:
= c^(yz + zx + xy) * (y-z)^yz * (z-x)^zx * c^(xy) / (x-y)^(yz + zx)
Therefore, the final expression for a^(yz) * b^(zx) * c^(xy) is c^(yz + zx + xy) * (y-z)^yz * (z-x)^zx * c^(xy) / (x-y)^(yz + zx).
Log a to the base e / (y-z) = log b to the base e / (z-x) = log c to the base e / (x-y)
Finding the Value of a^(yz) * b^(zx) * c^(xy):
Let's solve the given equations one by one and then calculate the final expression.
Solving the Given Equations:
1. Log a / (y-z) = log b / (z-x)
Using the property of logarithms, we can rewrite the equation as:
a / (y-z) = b / (z-x)
This implies a = b * (y-z) / (z-x)
2. Log b / (z-x) = log c / (x-y)
Similarly, rewriting the equation gives:
b / (z-x) = c / (x-y)
This implies b = c * (z-x) / (x-y)
3. Substituting the value of b from equation 2 into equation 1:
a = (c * (z-x) / (x-y)) * (y-z) / (z-x)
= c * (y-z) / (x-y)
4. Now, we need to find a^(yz) * b^(zx) * c^(xy):
Substituting the values of a, b, and c into the expression:
a^(yz) * b^(zx) * c^(xy)
= (c * (y-z) / (x-y))^(yz) * (c * (z-x) / (x-y))^(zx) * c^(xy)
= c^(yz) * (y-z)^yz / (x-y)^yz * c^(zx) * (z-x)^zx / (x-y)^zx * c^(xy)
Final Expression:
= c^(yz + zx + xy) * (y-z)^yz * (z-x)^zx * c^(xy) / (x-y)^(yz + zx)
Therefore, the final expression for a^(yz) * b^(zx) * c^(xy) is c^(yz + zx + xy) * (y-z)^yz * (z-x)^zx * c^(xy) / (x-y)^(yz + zx).
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Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.?
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Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.?.
Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Log a to the base e whole dived by( y-z )= log b to the base e whole divded by( z-x) = log c to the base e whole divided by (x-y) and find a raise to power (y z)^2 multiply b to the power (z x)^2 multiply c to the power(x y)^2.?.
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