Write the expression as a logarithm of a single expression.

Question

Write the expression as a logarithm of a single expression.

 

 

Log √¯x + Log x¹¹ - Log x = ?

 

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

 

Answer 1

 Log √X + Log X¹¹ - logX =

 

 

   Log ( √X . X¹¹ / X)  = log ( X ¹⁰  . √X ) 

 

                                 = log X ^ (21/2)= log  √(X^21 )

Answer 2

Hi Keith;

log √x + log x¹¹ - log x

log x^1/2 + 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 x^1/2 + 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 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 x¹ to eliminate any confusion.

log x^{11 1/2}- log x¹

log (x^{11 1/2})/x¹

We will subtract...(11 1/2 - 1)

log x^{10 1/2}

10 1/2 log x