Express in terms of sums and differences of logarithms

Question

a) ln√ab^3

 

 

b)log₆[(x/y⁷)⁴]

Answer 1

a) ln√ab^3

 

Assuming this is ln√(ab³)

 

= ln(ab³)^1/2

= (1/2)ln(ab³)

= (1/2)[ln a + ln b³]

= (1/2)[ln a + 3ln b]

 

or (1/2)ln a + (3/2)ln b

Answer 2

a)

Using grouping symbols to clarify.

b)

log₆[(x/y⁷)⁴]

log₆(x⁴ / y²⁸)

log₆ x⁴ - log₆ y²⁸

4 log₆ x - 28 log₆ y