Write the expression as a logarithm of a single expression.

Log √¯x + Log x

^{11 }- Log x = ?(type positive exponents only. Use integers or fractions for any numbers in the expression.)

Write the expression as a logarithm of a single expression.

Log √¯x + Log x^{11 }- Log x = ?

(type positive exponents only. Use integers or fractions for any numbers in the expression.)

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Middletown, CT

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...

A*unt 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

Woodland Hills, CA

Log √X + Log X^{11} - logX =

Log ( √X . X^{11} / X) = log ( X ^{10 } . √X )

= log X ^ (21/2)= log √(X^21 )

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