How do i express y as a function of x
Logy=1/3(logx-log27)
To express y as a function of x using the given equation, we can follow these steps:
Step 1: Simplify the right side of the equation.
- Use the properties of logarithms to simplify the equation:
logy = 1/3(logx - log27)
- We can simplify the right side further by applying the logarithmic property, log(xy) = log(x) + log(y), and log(x/y) = log(x) - log(y).
logy = 1/3(logx - log27)
= 1/3(logx - log(3^3)) [Since 27 = 3^3]
= 1/3(logx - 3log3) [Applying log(xy) = log(x) + log(y)]
Step 2: Use the power rule of logarithms.
- The power rule states that log(x^n) = n*log(x).
- Applying this rule to the equation, we get:
logy = 1/3(logx - 3log3)
= 1/3(logx - log(3^3))
= 1/3(log(x/3^3)) [Applying log(x/y) = log(x) - log(y)]
= log((x/3^3)^(1/3)) [Using the power rule]
Step 3: Remove logarithms and express y as a function of x.
- To remove the logarithm, we can rewrite the equation in exponential form:
y = (x/3^3)^(1/3)
Therefore, the expression y as a function of x is:
y = (x/27)^(1/3)
That's it! Now you have expressed y as a function of x.