Write as a single logarithm: 3log x - 1/2 log y

Question

Write as a single logarithm: 3 log x - 1/2 log y

Answer 1

Using the logarithmic property a log b = log(b^a), we have

3 log x = log(x³)

1/2 log y = log(y^1/2)

From this we can write 3 log x - 1/2 log y = log(x³) - log(y^1/2)

Using the logarithmic property log a - log b = log(a/b), we can write

3 log x - 1/2 log y = log(x³) - log(y^1/2) = log(x³/y^1/2)