Hi Keith;
log √x + log x^{11}  log x
log x^{1/2} + log x^{11}  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 x^{1/2} + log x^{11} 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 x^{11 1/2} log x
Let's apply the principle...
log a/b=log a  log b
Let's also rewrite log x to log x^{1} to eliminate any confusion.
log x^{11 1/2} log x^{1}
log (x^{11 1/2})/x^{1}
We will subtract...(11 1/2  1)
log x^{10 1/2}^{
}
10 1/2 log x
2/17/2014

Vivian L.
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