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Mathematics 14 Online
OpenStudy (anonymous):

8= 5+ 2log(x/4)....solve for x

OpenStudy (anonymous):

subtract 5 from both sides of the equation and post what you got.

OpenStudy (anonymous):

3=2log(x/4)

OpenStudy (anonymous):

divide 2 on both sides and post what you got.

OpenStudy (anonymous):

3/2=log(x/4)

OpenStudy (anonymous):

now take inverse log on both sides.

OpenStudy (anonymous):

i dont know how

OpenStudy (anonymous):

okay, \[\log_{a}x =y \rightarrow x = y^{a} \]

OpenStudy (anonymous):

so x=3/2^4

OpenStudy (anonymous):

no, the natural log, ln is generally to the base e, that is, \[\ln =\log_{e} \] whereas when you see log in a problem, it generally to the base 10. that is, \[\log_{} = \log_{10} \]

OpenStudy (anonymous):

im confused on what it would look like

OpenStudy (anonymous):

so, if you know that \[\log_{a} x=y→x=y^{a}\] and

OpenStudy (anonymous):

\[\log_{10}(x/4) = 3/2 \rightarrow x/4 = ?\]

OpenStudy (anonymous):

3/2^10

OpenStudy (anonymous):

whoops my mistake. \[\log_{a}x = y \rightarrow x = a ^{y} \]

OpenStudy (anonymous):

ok got it thanks

OpenStudy (anonymous):

you are welcome.

OpenStudy (anonymous):

for example, \[\log_{10}1000 = 3 \] why? because \[10^{3} = 1000\]

OpenStudy (anonymous):

i have another

OpenStudy (anonymous):

similarly \[\log_{10}64 = 1.80 \] why? because \[10^{1.8} = 64\]

OpenStudy (anonymous):

do you understand the concept of logarithms?

OpenStudy (anonymous):

yes i do property of logs

OpenStudy (anonymous):

not the properties, do you understand the fundamental concept of logs?

OpenStudy (anonymous):

log base 5 (3x+10) -3 log base 5 (4)=2.......yes i do!

OpenStudy (anonymous):

okay great!

OpenStudy (anonymous):

could u help me with that problem

OpenStudy (anonymous):

log a + log b = ?

OpenStudy (anonymous):

log a time b

OpenStudy (anonymous):

and log a - log b = ?

OpenStudy (anonymous):

divide

OpenStudy (anonymous):

a log b?

OpenStudy (anonymous):

logb^a

OpenStudy (anonymous):

ok so what is 3 log 4?

OpenStudy (anonymous):

64

OpenStudy (anonymous):

what?

OpenStudy (anonymous):

are you sure?

OpenStudy (anonymous):

log64

OpenStudy (anonymous):

okay good so what is log(3x+10)-log64?

OpenStudy (anonymous):

log has a base of 5 on both

OpenStudy (anonymous):

\[\log_{5} \]

OpenStudy (anonymous):

yes.

OpenStudy (anonymous):

so what?

OpenStudy (anonymous):

im confused from there

OpenStudy (anonymous):

log(3x+10)/64

OpenStudy (anonymous):

okay, when you say \[\log A+\log B = \log(A*B) \], what you really mean is \[\log_{x}A+\log_{x}B = \log_{x}AB \]

OpenStudy (anonymous):

well division

OpenStudy (anonymous):

so only if your bases are the same, you can perform logarthmic arithmetic.

OpenStudy (anonymous):

yea

OpenStudy (anonymous):

so your equation now becomes \[\log_{5}((3x+10)/64 ) = 2\]

OpenStudy (anonymous):

we know that \[\log_{a}x = y \rightarrow x = a ^{y}\]

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

so what is 3x+10/64 = ?

OpenStudy (anonymous):

25

OpenStudy (anonymous):

so 3x+10 = ?

OpenStudy (anonymous):

ok got it thank u again

OpenStudy (anonymous):

you are welcome.

OpenStudy (anonymous):

ok so i am stuck on another i am at x+4(x-1)=36

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