Question

Let log,4 = 3; log,C' = 2; log₂D = 5log (C²),10% ?What is the value ofA. -11OB. There isn't enough information to answer the question.C. 2D. -15,378

Answer 1

Explanation

We are given the following:

We are required to determine the value of:

3We know that the multiplication and division laws of logarithm state:

Therefore, we have:

`\begin{gathered} \log_b((A^5C^2)/(D^6))=\log_b(A^5C^2)-\log_bD^6 \\ =\log_bA^5+\log_bC^2-\log_bD^6 \end{gathered}`

We also know that the power law of logarithm states:

Therefore, we have:

`\begin{gathered} \Rightarrow\log_bA^5+\log_bC^2-\log_bD^6 \\ =5\log_bA+2\log_bC-6\log_bD \\ Substituting\text{ }their\text{ }values \\ =5(3)+2(2)-6(5) \\ =15+4-30 \\ =-11 \end{gathered}`

Hence, the answer is -11.