How to solve this natural log?

Question

How does: ln2 + 2/3 ln4 = 7/3 ln2

show the steps

thanks

Answer 1

I hope its (2/3) ln4 not 2/(3ln4)

(2/3) ln4 = (2/3) ln (2^2)= 2(2/3) ln2 = (4/3)ln2

so give expr = {1+(4/3)}ln2 =(7/3) ln 2.

{1+(4/3)} = 7/3 should not be difficult even without a calculator.

Answer 2

0.693 + 0.924 =7/3(0.693)=1.61734=1.617 o.k.

Answer 3

ln2 + 2/3 ln4 = 7/3 ln2

ln2 + 2/3 ln2^2 = 7/3 ln2

ln2 + 4/3 ln2 = 7/3 ln2

7/3ln2=7/3ln2

Answer 4

You are being asked to understand the following principle:

ln(aⁿ) = n·ln(a)

ln(2) + (2/3) ln(4)

ln(2) + (2/3) ln(2²) <----- applying the power rule here gives you:

ln(2) + (2)(2/3) ln(2)  

ln(2) + (4/3) ln(2)

(3/3) ln(2) + (4/3) ln(2) = (7/3) ln(2)

Answer 5

Assuming :-

ln 2 + (2/3) ln 4

ln 2 + (2/3) ln 2²

ln 2 + (4/3) ln 2

(7/3) ln 2 as required