Question

40. Rewrite each expression as an equivalent expression containing only one logarithm.

b. ln(xy) − ln(x/y)

Answer 1

ln(xy) - ln(x/y) = 2ln(y)

Explanation:

To solve this problem one must have knowledge about properties of logarithmic functions.

According to the product property:

`ln(xy) = ln(x) + ln (y)`

According to the quotient property:

`ln(x/y) = ln(x) - ln (y)`

Combining both properties it is possible to rewrite the expression as:

`ln(xy) - ln(x/y) = ln(x) + ln (y) - (ln(x) - ln(y))`

`ln(xy) - ln(x/y) = 2ln (y)`