Apply logarithms to create a linear relationship:
((x^3)(y^1.5))/(z^.5)=k
take the log of both sides:
3logx+1.5logy-.5logz=logk
3*log(x)+1.5log(y)-0.5log(z)=log(k)
To create a linear relationship from the given equation, we can apply logarithms. Specifically, we can take the logarithm of both sides of the equation.
Starting with the original equation:
((x^3)(y^1.5))/(z^.5) = k
Taking the logarithm of both sides using a base of your choice (commonly used bases are 10 or e):
log(((x^3)(y^1.5))/(z^.5)) = log(k)
Now, we can simplify the left side of the equation using logarithmic properties. Applying the logarithm to each term separately:
log(x^3) + log(y^1.5) - log(z^.5) = log(k)
Using the power rule of logarithms, we can bring down the exponents as coefficients:
3 log(x) + 1.5 log(y) - 0.5 log(z) = log(k)
At this point, we have transformed the equation into a linear relationship. The equation is now in the form:
A log(x) + B log(y) + C log(z) = D
where A = 3, B = 1.5, C = -0.5, and D = log(k).
By doing this transformation, we have replaced the original equation with a linear equation involving logarithms of the variables. This can be useful for analyzing the relationship between the variables x, y, and z in a linear manner.