1.Write the following as the sum or difference of logarithm. Simplify as much as

Annette Arroyo

Annette Arroyo

Answered question

2021-10-15

Write the following as the sum or difference of logarithm. Simplify as much as possible. Assume the variables represent positive real numbers. 
log5{x3y4z}

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-10-16Added 117 answers

Step 1
Logarithmic functions and exponential functions are considered to be the inverses of each other as one function can always be represented in another functions form.
For example if we have the function y=ax , then taking log on both sides will give is logy=x×loga. Hence, the original exponential function is converted into logarithmic function by using properties of logarithms. Similarly, we can convert logarithmic function to an exponential function.
Step 2
The given logarithm is log5{x3y4z}
Simplifying the given function using properties of logarithms.
log5{x3y4z}=log(x3y4z)15=15log(x3y4z)
=15[log(x3)log(y4z)]
=15[log(x3)log(y4)log(z)]
=15[3logx4logylogz]
=35logx45logy15logz}
The simplified form of function is given as 35logx45logy15logz
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-03Added 2605 answers

Answer is given below (on video)

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