##ln(a^20/b^4)## or ##4ln(a^5/b)##.

##20lna=lna^20## by the rule ##bloga=loga^b##.

Similarly, ##4lnb=lnb^4## by the same rule.

So now we have ##20lna-4lnb=lna^20-lnb^4##.

Now, using the rule ##loga-logb=log(a/b)##, we can rewrite this as ##ln(a^20/b^4)##.

If you like, you can write this as ##ln((a^5/b)^4)##, which can be rewritten as ##4ln(a^5/b)##.

You can plug numbers in to these rules to make sure they work. For example, ##log_2 32-log_2 8=5-3=2##. If you use the division rule, you get ##log_2 32-log_2 8=log_2(32/8)=log_2(4)=2##.

More generally, we can show this rule and the others to be true. I will show that ##loga+logb=log(a*b)##.

Start with ##y=lna+lnb##.

Exponentiate both sides to get ##e^y=e^(lna+lnb)##.

Through rules of exponents, the right side can be rewritten to get ##e^y=e^lna*e^lnb##.

Since ##e^lnx=x## (if you’re confused why, say something) we get ##e^y=a*b##.

To finish, take the natural log of both sides to get ##y=ln(a*b)##.

Similar things can be done to prove the other rules true.

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

How do you correctly conjugate an -ar ending verb in espanol?

How to Conjugate Verbs with An –ar EndingThe infinitive is the base form of a verb. All infinitive verbs end with an –er, -ir, or in our casean –ar.For the most part, most verbs in Spanish…

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

How do you define how managerial accounting differs from financial accounting. Addressing the diverse users of managerial and of financial accounting and provide examples of how at least five users would utilize accounting information. 

Illustrate how managerial accounting information assists managers in performing the roles of planning, directing, and controlling by providing an example of each. 

Briefly explain how the Sarbanes-Oxley Act (SOX) affects management accountants specifically, and answer this question: In your opinion, is SOX enough to deter unethical accounting practices internally? Be specific and support your opinion with academic research.

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

how do you design a research study by:- 

1• developing one specific research question and related hypothesis

2• Discuss the importance/significance of your research topic.

3 • Describe your dependent and independent variables to be tested in your study.

4• Describe how you define and measure the variables.

5• Describe other potential explanatory (control) variables in your analysis.

6• Identify your research subjects (persons or things). What or who will be studied?

7 • Describe how you will select the subjects and how you will reach them.

 8• Describe the type of sampling techniques that you will use to select a sample.

 9• Explain why you have selected that sampling method.

10• Describe in detail how you will actually collect the data for your study.

 11• Explain why you choose the method(s)

12• Briefly describe how you will test your hypothesis using the data you collect.

13• Discuss any issues or limitations of your study

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"