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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.
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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
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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
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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?
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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
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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?
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OpenStudy (anonymous):
logb^a
OpenStudy (anonymous):
ok so what is 3 log 4?
OpenStudy (anonymous):
64
OpenStudy (anonymous):
what?
OpenStudy (anonymous):
are you sure?
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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.
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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
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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
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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.
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