Another Log Question?

Question

Heys guys I have another question dealing with logs. How would you evaluate this question?

log base 3 of (27 * 81^(1/3) ) + log base 5 of (125 * 5^(1/4) )

Answer: 72/11

Any help would be greatly appreciated!

Answer 1

Write the first expression as powers of 3:
27 * 81^(1/3) is the same as:
= 3^3 * 3^4^(1/3)
= 3^3 * 3^(4/3)
= 3^(3 + 4/3)
= 3^(13/3)
Taking log base 3, you get 13/3.

And write the second expression as powers of 5:
125 * 5^(1/4)
= 5^3 * 5^(1/4)
= 5^(3 + 1/4)
= 5^(13/4)
Taking log base 5, you get 13/4

So this simplifies to:
13/3 + 13/4

Common denominator of 12:
52/12 + 39/12

= 91/12

I agree with everyone else; you must be looking at the wrong answer sheet.

Answer 2

take it apart first:

log base 3 of 27 + 1/3 log base 3 of 81 + log base 5 of 125 + 1/4 log base 5 of 5

= 3 + 1/3 (4) + 3 + 1/4 (1)
= 6 + 4/3 + 1/4
= 91/12

Well, I don't get the 72/11, and certainly don't see how you could. You're just expanding, then using the definition. It's pretty straight forward.

Answer 3

I don't get that answer.

log base 3 of (27* 81^(1/3)
= log base 3 (27) + 1/3 log base 3 (81)
=3 + 1/3(4) =3 + 4/3 = 13/3

log base 5 (125 * 5^(1/4))
= log base 5 (125) + 1/4 log base 5of(5)
= 3 + 1/4(1)
=13/4

13/3 + 13/4 = 52/12 + 39/12 = 91/12

Answer 4

simplifies to:
log(3,27) + 1/3 log(3,81) + log(5,125) + 1/4 log(5,5)
3 + 4/3 + 3 + 1/4
i got 7 and 7/12, or 91/12

Answer 5

log(3)27+LOG(3)81^(1/3)+log(5)125+log(5)5^(1/4)=
3+1/3(log(3)81+3+1/4log(5)5=
6+(1/3)(4)+1/4=
25/4+4/3=91/12

Answer 6

yeah totally