Let u lnx and v lny for x 0 and y 0 Write ln x3 7 Square

Let u = ln(x) and v = ln(y), for x > 0 and y > 0. Write ln (x^3 7 Squareroot y^2) in terms of u and v. Find the domain, the x-intercept and asymptotes. Then sketch the graph for f(x) = ln(x - 3).

Solution

u= ln (x)       v= ln(y)

ln (x³ seventh root of y²)

ln(x³y^2/7)

We have to use the following log properties

log a b = log a + log b

log a^b = b log a

Applying these properties

ln x³ + ln y^2/7

3 ln x    +     (2/7) ln y

3u + (2/7)v