Suppose that 𝐴=ln𝑥 , 𝐵=ln𝑦 and 𝐶=ln𝑧 .

Question

Suppose that  𝐴=ln𝑥  ,  𝐵=ln𝑦  and  𝐶=ln𝑧 .

Write ln(𝑦^3⋅√𝑥/𝑧^2⋅𝑒^4) in terms of  𝐴,  𝐵  and  𝐶  .    

Show your work.

Your answer should not include any logarithms.

Answer 1

Write ln(𝑦³⋅√𝑥/𝑧²⋅𝑒⁴) in terms of 𝐴, 𝐵 and 𝐶.

ln(𝑦³⋅√𝑥/𝑧²⋅𝑒⁴) = 3ln𝑦 + ½lnx – 2lnz – 4

This result comes from applying the product, quotient, and power rules of logarithms. Illustrating the details of applying these rules might be the show your work part of the answer.

Since 𝐴 = ln𝑥, 𝐵 = ln𝑦 and 𝐶 = ln𝑧

we substitute to get the required form that does include any logarithms

Answer

ln(𝑦³⋅√𝑥/𝑧²⋅𝑒⁴) = 3𝐵 + ½𝐴 – 2𝐶 – 4