The expansion for \log \frac{x^{2}y^{3}}{\sqrt[3]{z}} using the properties

Brennan Flores

Brennan Flores

Answered question

2021-09-19

The expansion for logx2y3z3 using the properties of logarithms and to represent the answer without exponents.

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-09-20Added 105 answers

Given:
The expression logx2y3z3.
Formula used:
Properties of logarithm:
1) logxn=nlogx
2) log(xy)=logx+logy
3) log(xy)=logxlogy
Calculation:
The given expression is logx2y3z3.
Since the expression on which log is applied is a fraction so we will apply property (3).
Which gives logx2y3z3=log(x2y3)logz3a)
Now, in log(x2y3), log is applied on product of two terms so we can apply property (2).
log(x2y3)=log(x2)+log(y3)
Also, z3 can be written as z13.
So, putting these in equation a) we get,
log(x2y3)=log(x2)+log(y3)log(z13)
Now, on right hand side, all the expressions have exponents so we can apply property (1).
This gives:
log(x2y3)=log(x2)+log(y3)log(z13.
This is the required result in which there is no exponent.
Conclusion:
These type of expressions can be simplified easily by applying the properties of log. When log is applied to product of two or more terms then corresponding log terms get added and similarly, when log is applied to a fraction then corresponding log terms get subtracted as given in the properties. These properties are used to simplify the expression.
If any log term has exponent then the exponent gets multiplied with the log term as discussed in the first property. This property is used to get rid of exponents.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?