Question

how would i condense Log8 12 + Log 8 X

Answer 1

Log(8*12) + Log (8X) ?

Answer 2

log laws Log(ab) = log(a) + log(b)

so do the reverse

\[\log _{8} (12x) = \log _{8}(12) + \log _{8} (x)\]

Answer 3

wait

Answer 4

okay i got that now but what about this one Log3(x^4y^6/4) that would be log3(x^4/4)-log3(y^6/4)

Answer 5

log(a) - log(b) = log(a/b)

so its

\[\log _{3} (x^4y^6) - \log _{3}(4)\]

Answer 6

then it becomes

\[\log _{3}(x^4) + \log _{3}(y^6) - \log _{3}(4)\]

Answer 7

woah

Answer 8

so you compleatly split it up?

Answer 9

but then log (a^x) = xlog(a)

so you question could be

\[4\log _{3}(x) + 6\log _{3}(y) - \log _{3}(4)\]

Answer 10

so those would be the quotient property then the power property? right?

Answer 11

quotient. product and power

Answer 12

okay

Answer 13

yet why is it a negative?