Solving Natural Logs: y=(sqrt(8x^4-5))/(x-1)

[mattmannmf]

I have the following function:

y= (sqrt(8x^4-5)) / (x-1)

take the natural log of both sides:

1) ln y= ln (sqrt( 8x^4-5) - ln (x-1)

OR

2) ln y= 1/2 ln(8x^4-5) - ln (x-1)

Which one is correct?

I know when i take the natural log of a/b its ln(a)- ln(b)... but also when i take the natural log of a^q its qln(a)...does that apply in this situation also or is it just ln(a)- ln(b)?

 

[cse63146]

The second would would be the correct option.

 

[mattmannmf]

ok i thought so...thanks!

 

[Mark44]

They're both correct. ln (sqrt( 8x^4-5)) = ln (8x^4 - 5)^1/2 = (1/2) ln(8x^4 - 5)

 

[HallsofIvy]

Both are correct. The second is simpler and more likely to be accepted as the "correct" way.