Question

expand each logarithm:
1. log x^3 y^5
2.log[base 7] 22xyz
3. log[base 4] 5 [square root x]
4.log 3m^4 n^-2
5. log [base 5] r/s
6. log [ base 3] (2x)^2

Answer 1

\[\log(ab)=\log(a)+\log(b)\]
\[\log(c^n)=n\log c\]

Answer 2

so wod the first answer be x log 3 + y log 5?
or log x ^3 + log x^5

Answer 3

\[\log x^3 y^5=\log x^3+\log y^5=\]

Answer 4

3 log x + 5 log y ?

Answer 5

thats right!

Answer 6

=D so how about the second one ?

Answer 7

wod it be 22 log [base 7] x + 22 log [base 7} y + 22 log [base 7} z ??

Answer 8

@UnkleRhaukus

Answer 9

\[\log_7 22xyz=\log_722+\log_7x+\log_7y+\log_7z\]

Answer 10

okay how about number 3.. i dont know how to solve it ?

Answer 11

\[\log_4 5 \sqrt x=\]

Answer 12

break the log into a sum of logs,
then use \(\sqrt x=x^{1/2}\)

Answer 13

okay so would it be : 1/2 log [base of 4 ] 5

Answer 14

not quite, your answer should have a sum of logs in it

Answer 15

like wat do u mean ? like 5 log [base of 4 ] + log 1/2

Answer 16

thats closer

Answer 17

log [base of 4] 5 + log 1/2 ?

Answer 18

thats is eve closer , but where did x go?

Answer 19

oh log [base of 4 ] 5 + log 1/2x

Answer 20

?

Answer 21

\[\log_4 5 \sqrt x=\log_4 5 +\log_4\sqrt x\]\[\qquad\qquad=\log_45+\log_4x^{1/2}\]\[\qquad\qquad=\log_45+\frac12\log_4x\]

Answer 22

oh okay i get it now , thank you :)
so th

Answer 23

so then number 4 wod be: log 3 + 4 log m + -2 log n ? is that right??

Answer 24

@UnkleRhaukus

Answer 25

you've got it!

Answer 26

for 5.

you have to remember that \[\frac 1s=s^{-1}\]

Answer 27

so it would be : log [base of 5] 1 + -1 log s ???

Answer 28

where did r go?

Answer 29

1 log [base of 5] r + -1 log [base of 5 ] s ????

Answer 30

thats good , but you dont need the ones (they are implied)
and +- can be written as just -

Answer 31

oh okay so it is : log [base of 5] r - log [base of 5 ] s ??

Answer 32

that is right .

Answer 33

okay thank you and then number 6 wod be : 2 log [base of 3] 2x + 2 log [base of 3] 2x ??? is that right ?

Answer 34

@UnkleRhaukus

Answer 35

check that one again

Answer 36

would it be : 2 log [base of 3] 2 + 2 log [base of 3] x

Answer 37

?

Answer 38

\[\LARGE\color{red}\checkmark\]

Answer 39

thank you so much for ur help :)

Answer 40

@UnkleRhaukus okay i have one more question : wat wod be the answer for
log[base 3] 7 ( 2x - 3) ^2

Answer 41

you tell me

Answer 42

wod the answer be :
2 log[base 3 ] 7 + 2 log[base 3] 2 + 2 log [base 3 ] x + 2 log [base 3] -3

Answer 43

@UnkleRhaukus

Answer 44

not quite

Answer 45

all you can do is this\[\log(a(b+c)^n)=\log(a)+\log(b+c)^n\]\[\qquad\qquad\qquad=\log(a)+n\log(b+c)\]

Answer 46

the log a sum (or difference) cannot be simplified

Answer 47

so it would be log [base 3] 7 + 2 log [base 3] ( 2x -3 ) ?

Answer 48

yeah that is all that can be done ,

great work

Answer 49

=D