Question

Write the expression as a single natural logarithm. 3 ln 2 + 6 ln y? can you explain how to solve it, i want to learn not just get it the easy way. thank you

Answer 1

Use these rules

y*ln(x)=ln(x^y)

and

ln(A)+ln(B)=ln(A*B)

Answer 2

So

y*ln(x)=ln(x^y)

3*ln(2)=ln(2^3)

3*ln(2)=ln(8)

Answer 3

and

6*ln(y)=ln(y^6)

Answer 4

both were found using the first rule

Answer 5

now we go from

3*ln(2)+6*ln(y)

to

ln(8)+ln(y^6)

Answer 6

now use the second rule to simplify ln(8)+ln(y^6)

Answer 7

ln(8)+ln(y^6) would be ln(8y^6) ? using the equation thank you very much this helped me understand!

Answer 8

correct, ln(8y^6) is the final answer