Question

Solve: log4x=log5+log(x-2)

Answer 1

@Owlcoffee could u help me?

Answer 2

Yes yes, dear friend.
first off, we have to know a couple of logarithm properties:
\[\log_{b} a +\log_{b} c=\log_{b} a.c\]
what this means is that if we have the sum of two numbers under the same logarithms base, we can take the product of those numbers and the result under the logarithms of the initial base and it won't alter the expression.
We can see a little example on the right side of the problem you posted:
\[\log4x=\log5+\log(x-2)\]
we can clearly see a sum of logarithms, so therefore:
\[\log4x=\log5(x-2)\]

Answer 3

Thank you! So , I'm on the right track, I've gotten that far. So then you distribute log 5(x-2) making it:
log4x=log5x-10
I just don't know what to do from there b/c i don't get what to do with the log4x side. or am i just going a tly different direction?
@owlcoffee

Answer 4

Okay let's now look at another property:
\[\log_{b} a=\log_{b} c <=> a=c\]
that means, if we have two expressions, on boths sides of the equality under a logarithm, I can ignore the logarithms and just work with the expressions.
Applying it to the problem:
\[\log4x=\log5(x-2)\]
that must mean, by the property I stated:
\[4x=5(x-2)\]
all you have to do now is find the value of "x" :)

Answer 5

@Owlcoffee I feel so stupid i cant solve for x which should be so simple. i keep getting x=10 but 10 is not one of the multiple choice answers. Please help me :(

Answer 6

Okay, let's first look at the expression:
\[4x=5(x-2)\]
let's do the distributive and operate:
\[4x=5x-10\]
\[-x=-10\]
\[x=10\]
what are the choices?

Answer 7

Oh wow ughhh.. I was looking at the wrong question. Thats why. I'm so sorry. Thank you for you help! :)

Answer 8

At your service ;)

Answer 9

can i ask you more questions if I have any? How long will you be on here? I promise I only ask questions if I can't figure them out myself for nothing.

Answer 10

Sure, just pm me or tag me on the pst, and I'll help.
I'll be on an hour or hour and half longer..

Answer 11

okay thank you so much! :)

Answer 12

@Owlcoffee
I just want to make sure I get this answer right.
Use properties of logarithms to condense the log expression. Write the expression as a single log whose coefficient is 1. Evaluate log expression if possible.
6lnx-1/7lny

Is it ln(x^6/y^1/7) or ln(x^6/7√y) ? I'm leaning more toward the second one.

Answer 13

Well, we would have to take the expression_
\[6lnx-\frac{ 1 }{ 7 }lny\]
and start tweaking it until we have any of the other results.

Answer 14

I used the quotient rule and the power rule

Answer 15

Let me see

Answer 16

i got\[\ln(x^6/\sqrt[7]{y})\]

Answer 17

is that right?

Answer 18

That's correct.

Answer 19

Very well done! :D

Answer 20

okay so same rules follow for next question:
\[\log_{6}24+\log_{6}9 \]
i got 3 as the answer or should i leave it as \[\log_{6}(216) \]

Answer 21

@Owlcoffee

Answer 22

That is correct, well done!

Answer 23

on the multiple choice tho there is an answer that says 3 and another that says \[\log_{6}(216) \] which one should i go with ? (its one or the other i really would hate to pick the wrong one)

Answer 24

They are both the same, but it's more correct to choose "3"

Answer 25

okay thank you. i hate tricky questions like that

Answer 26

It's very common in math teachers haha

Answer 27

i got an 87 on my math assignment thanks so much for all ur help! :)))