Question

WILL FAN AND MEDAL
write the expression as a single logarithm 5logby + 4logbx

i have no idea how to do this

answers posted in a sec

Answer 1

HI!!

Answer 2

no need to post the answers

Answer 3

you will use two facts

Answer 4

hi! :)

Answer 5

first one is that \[n\log(x)=\log(x^n)\]
write each like that first

Answer 6

second is that \[\log(x)+\log(y)=\log(xy)\] use that second

Answer 7

blog(y) = log(x^4) ?

Answer 8

no don't set them equal
first rewrite \[5\log(y)\] as \[\log(y^5)\]
now you do the second one \[4\log(x)\]

Answer 9

log(x^4)

Answer 10

right so now we are at this step \[5\log(y)+4\log(x)=\log(y^5)+\log(x^4)\]

Answer 11

now the sum of the logs is the log of the products, which is an english way of saying \[\log(A)+\log(B)=\log(AB)\]

Answer 12

so write the log of the product of \(y^5\) and \(x^4\)

Answer 13

log(xy^9) ?

Answer 14

@misty1212

Answer 15

no

Answer 16

\[y^5x^4\neq xy^9\]

Answer 17

\[x^4y^5=x^4y^5\]that is all

Answer 18

so put that inside the log

Answer 19

i dont understand how

Answer 20

@misty1212

Answer 21

just write it \[\log(x^4y^5)\]

Answer 22

so is that the answer? @misty1212

Answer 23

yes

Answer 24

so it would be b, right?

Answer 25

post your options

Answer 26

yes

Answer 27

thank you!!

Answer 28

np