Question

please help log8 x^3=-2
log(x-3)+logx=log4

Answer 1

do you know the various log rules?

Answer 2

if not, you can find them here: http://www.purplemath.com/modules/logrules.htm
they should help you solve this.

Answer 3

please ask if you need any clarification

Answer 4

still cant understand those rules sorry

Answer 5

which part confuses you?

Answer 6

the one to solve the first problem

Answer 7

ok, I tihkn your first problem is:\[\log_8(x^3)=-2\]correct?

Answer 8

*think

Answer 9

yes

Answer 10

right, lets break this up into parts.
firstly, if you have:\[\log_a(x^b)\]then this can be simplified to:\[b*log_a(x)\]

Answer 11

so we simplify you 1st equation to:\[3\log_8(x)=-2\]

Answer 12

I am solving for x

Answer 13

next we can divide both sides by 3 to get:\[\log_8(x)=\frac{-2}{3}\]

Answer 14

now we can use another log rule that states if:\[\log_a{b}=c\implies b=a^b\]

Answer 15

so, using this, we get:\[x=8^{\frac{-2}{3}}\]
this can be simplified further

Answer 16

we can use this fact:\[a^{-b}=\frac{1}{a^ab\]to get:\[x=\frac{1}{8^{\frac{2}{3}}}\]

Answer 17

now, \(8=2^3\), so \(8^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=2\)
so \(8^{\frac{2}{3}}=2^2=4\)

Answer 18

so finally, we get:\[x=\frac{1}{4}\]

Answer 19

do you understand the various steps above?

Answer 20

a bit confusing

Answer 21

which step was confusing?

Answer 22

I can try and explain it in more detail

Answer 23

I will try to do the other then I will let you know

Answer 24

ok - good luck

Answer 25

I did this one take a look please: logx 16=5
X^5=16
x=\[\sqrt[5]{16}\]

Answer 26

correct

Answer 27

you're a PRO now!

Answer 28

what about this one: log(x-3)+logx=log4
have you been able to do this yet?

Answer 29

doing it now

Answer 30

keep in mind that if:\[\log(a)=\log(b)\implies a=b\]

Answer 31

[(x-3)x]=4
(x-3)x=10^4
x^2-3x=10000 got scared by this big number am I on the right way?

Answer 32

:-)

Answer 33

not quite

Answer 34

you are correct up to:
(x-3)x = 4

Answer 35

your next step after that was incorrect. where did you get the 10^ from?

Answer 36

log of natural number

Answer 37

you should have ended up with:\[\log(x(x-3))=\log(4)\]which then leads to:\[x(x-3)=4\]

Answer 38

remember what I said above:\[\log(a)=\log(b)\implies a=b\]

Answer 39

if the log of 'a' equals the log of 'b', then 'a' must be equal to 'b'

Answer 40

do you understand this step?

Answer 41

so is it going to be something like this: x^2-3x-4=0

Answer 42

exactly

Answer 43

this can be factorised

Answer 44

do you know to factorise?

Answer 45

yes

Answer 46

so what do you get for this equation?

Answer 47

(x-4) (x+1)

Answer 48

perfect, so the solutions for 'x' are?

Answer 49

x=4 or x=-1

Answer 50

correct - well done - you are a quick learner.
many people would have given up by now.
have faith in your abilities and you will be surprised by what you can achieve!

Answer 51

thanks for you help

Answer 52

you're welcome.

Answer 53

can you verify this one please: 3log x-1/2log y-log z
logx^3-logy^1/2-logz
logx^3-log\[\sqrt{y}-logz
log x^3/z sqrt y