Simplify the following expressions. Your answers must be exact and in simplest form.

Question

(a) log8(8^−5x−10)=

(b) 12^log12(−5+7q)=

(c) log4(64^k)=

(d) 3^3log3(10−10log3^3)=

Answer 1

I'll do one. You just need to remember that

log(ab) = log(a) + log(b)
log(a^n) n log(a)

So, (c) can be done as follows:
log4(64^k)
= log4(4^3^k)
= log4(4^(3k))
= 3k

since log_b(b) = 1 for any b

I think you have garbled (d).

Try using some parentheses to clarify, or try typing it in at wolframalpha.com to see how it interprets it.

It will recognize log_3(x) as log₃x

Answer 2

ok thx!