Expand into several logarithms: \ln\left(\frac{x^2y^3}{z^5}\right)

Ava-May Nelson

Ava-May Nelson

Answered question

2021-10-26

Expand into several logarithms:
ln(x2y3z5)

Answer & Explanation

Mitchel Aguirre

Mitchel Aguirre

Skilled2021-10-27Added 94 answers

Step 1
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
Division rule logamlogan=loga(mn)
Step 2
The given expression is ln(x2y3z5) , use product and division rule to expand the given expression ,
ln(x2y3z5)=ln(x2y3)ln(z5) (using division rule)
=ln(x2)+ln(y3)ln(z5) (using product rule)
Therefore, expand version of ln(x2y3z5) is equal to ln(x2)+ln(y3)ln(z5)

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