Calculus Question

Question

Logb square root x (x + 4)/x2

 

 

Write each expression as a sum, difference or multiple of single logarithms.

 

I don't know how to answer the question please explain step by step to get the answer

 

Answer 1

You want to evaluate

 

Logb square root x (x + 4)/x2

 

I interpret this as

 

Log_b[sqrt[x(x+4)/x²]]=Log_b[[x(x+4)/x2]^(1/2)]

 

Use the following rules

 

Log(xy)=Log(x)+Log(y)

 

Log(x^y)=yLog(x)

 

You get

 

=Log_b[[x(x+4)/x²]^(1/2)]=(1/2)[Log_b(x)+Log_b(x+4)-2Log_b(x)]=(1/2)[Log_b(x+4)-Log_b(x)]

 

Check the algebra to make sure there are no errors.

 

 

 

Answer 2

I cannot answer the full question due to my confusion on your notation of the problem but perhaps I can give some important hints.

When dealing with logarithms, some functions can be split into two or combined. 

For example, If you have logb (x/x+9) this can be taken and rewritten as logb(x)-logb(x+9). This division function can be separated to make one function minus the other.

Similarly, If the problem had been logb (x)(x+9) this can be taken and rewritten as logb(x)+logb(x+9).

The opposites of these functions can also be done.

In order to complete your problem you must first identify which functions are happening and then decide which expansions are necessary to the problem.

I hope his was helpful!