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Write the expression as a logarithm of a single expression.

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2 Answers

Hi Keith;
log √x + log x11 - log x
log x1/2 + log x11 - log x
Should we begin with the addition or subtraction?
The algebraic order of operations is...
Parentheses
Exponential
Multiplication
Division
Addition
Subtraction
The acronym for this is PEMDAS, also remembered as...
Please
Excuse
My
Dear
Aunt
Sally
 
Aunt Sally...addition before subtraction.
log x1/2 + log x11 -log x
Let's apply the principle...
log ab=log a + log b
log x[(1/2)+(11)]- log x
We will add (1/2) + 11...
log x11 1/2- log x
Let's apply the principle...
log a/b=log a - log b
Let's also rewrite log x to log x1 to eliminate any confusion.
log x11 1/2- log x1
log (x11 1/2)/x1
We will subtract...(11 1/2 - 1)
log x10 1/2
10 1/2 log x
 
 
 
 
 

Comments

Keith;
As per Parviz's answer, I corrected a mistake.  I eliminated the 2 of 2x.  I apologize.

Comment

 Log √X + Log X11 - logX =
 
 
   Log ( √X . X11 / X)  = log ( X 10  . √X ) 
 
                                 = log X ^ (21/2)= log  √(X^21 )