Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 20) ln 10 21) ln 7 20

Question

Suppose that ln 2 = a and ln 5 = b. Use properties of
logarithms to write each logarithm in terms of a and b.

 

ln 10

ln⁷√20

Answer 1

Hi Couva,

 

ln 10 = ln (2*5) = ln 2 + ln 5 = a + b  (used the product identity of logs)

 

ln 7√20 = ln (20)^1/7 = 1/7ln 20 = 1/7(ln (2*10)) = 1/7(ln 2 + ln 10) = 1/7(a + (a+b))

(remember we found that ln 10 = a+b above)

= 1/7(2a + b)