Question

Which expression is equivalent to log12 x^4sqrt x^3-2/(x+1)^5

A 4log12 x+1/2log12 (x^3-2)-5log12 (x×1)

B 4log12x+1/2log12x^3/2-5log12x+log12 1

C Log124x+1/2log12 (x^3-2)-5log12 (x)+1

D 4Log12x+1/2log12 (x^3-2)-5log12 (x+1)

Answer 1

D on edge

Explanation:

i just took the test

Answer 2

The given expression is:


`log_(12)( \frac{x^(4) \sqrt{ x^(3)-2 } }{(x+1)^(5)} )`

Using the rules of log:


`log(ab)=log(a)+log(b) \\ \\ log( (a)/(b) )=log(a)-log(b) \\ \\ log(a)^(x)=xlog(a)`

We can simplify the given expression as:


`log_(12)( x^(4) ) +log_(12)( \sqrt{ x^(3)-2 } ) -log_(12)((x+1)^(5) ) \\ \\ =log_(12)( x^(4) ) +log_(12)((x^(3)-2)^{ (1)/(2) } ) -log_(12)((x+1)^(5) ) \\ \\ =4log_(12)(x)+ (1)/(2) log_(12)( x^(3)-2 )-5log_(12)(x+1)`

This is the simplified form the of the given expression.

Thus, option D gives the correct answer