Use the properties of Logarithims to expand the expression:

Question

⁶_√6+x/x⁵

 

Thanks so much for your assistance

Answer 1

use this rule      ln (A / B) = ln A - ln B

 

then brings the exponents down to the front making them coefficients (this is the power rule)

 

ln [ (6+x)^1/6 / x⁵] = ln (6+x)^1/6 - ln x⁵ = 1/6 ln (6+x) - 5 ln x

Answer 2

I think you've got a typo, what you've written is equal to 6√6+x/x5 = 6√6 + 1/5 

 

Now, you know 2 = √4 < √6 < √9 = 3.  Now I'm gonna guess that √6 ~ 2.2 'cause 1/5 = .2.

 

Checking 2.2 * 2.2 = .44 + 4.4 = 4.84.

 

Well, not a great a guess. How's about 2.4 (not that I've got my brain screwed in straight, I remember that 25 * 25 = 625).

 

2.4 * 2.4 = .96 + 4.8 = 5.76, which ain't that much closer to 6 than 6.25 is.   So call it 6*2.42 + .2 ~14.75

 

Not really sure what the point of bringing logarithms to bear is.