Algebra 2 once more

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I have more answers that I would like checked. Also, there is one that I'm really confused about. I appreciate any help. :)

Rewrite as the log of a single number.
1) 8 ln 2 = ln(2^8)
2) log 42 - log 6 = log 36 (I think this one may be wrong).

Evalute each expression w/o a calculator.
3) log(subscript 12) (superscript 5)square root of 12 = 0.2
4) log(subscript 6) 216 = 3

The one I'm not sure how to do looks like this: log(subscript 4)s^3 = 8. I'm supposed to solve for s. It would be great if someone could show me the steps for how to solve it.

#1 is right
#2, no
log A - log B = log (A/B)
so log 42 - log 6 = log 7

#4 is good

#5..... is this what you mean? (log12 √12)5 ?

if so, then you would have (1/2)^5
= 1/32

for log(subscript 4)s^3 = 8

4^8 = s^3
s^3 = 65536
s = appr. 40.317 (I took the cube root)


Actually, the 5 is before the square root symbol. I'm just not sure how to type it out...!

then my interpretation was right
remember that

log2 x is the same as (log x)2

Riiight ok I remember that now. Thanks again for the help. :)

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