Use the properties of the natural logarithms to simplify the

Eichowa4

Eichowa4

Answered question

2021-11-21

Use the properties of the natural logarithms to simplify the following expressions:
a)lnsinθlnsinθ5

Answer & Explanation

Ceitheart

Ceitheart

Beginner2021-11-22Added 14 answers

Step1
Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms.
There are various rules involved in performing logarithmic operations, some required for question are as follows
Product rule  logam+logan=logamn
Product rule  logamlogan=loga(mn)
Step 2
The given expression is ln(sinθ)ln(sinθ5) , use division rule to simplify the expression
ln(sinθ)ln(sinθ5)=ln(sinθsinθ5)=ln5
Therefore, simplified version ln(sinθ)ln(sinθ5)  is equal to  ln5
Hiroko Cabezas

Hiroko Cabezas

Beginner2021-11-23Added 18 answers

lnsinθlnsinθ5=lnsinθ(lnsinθln5)=ln5

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