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OpenStudy (anonymous):
\[\log _{3}27\]
OpenStudy (cwrw238):
this means 3 ^x = 27
x = value of the log
OpenStudy (anonymous):
?
OpenStudy (anonymous):
x=3?
OpenStudy (cwrw238):
3 ^ 3 = 27 right?
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OpenStudy (cwrw238):
yes
OpenStudy (anonymous):
ok :)
OpenStudy (cwrw238):
the definition of a log is the exponent whci takes the base to the given number
OpenStudy (anonymous):
wait then whats \[\log _{2} 32\]
OpenStudy (cwrw238):
eg 10^2 = 100
so log (10) of 100 = 2
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OpenStudy (cwrw238):
what power must 2 be taken to in order to get 32s
OpenStudy (cwrw238):
* 32?
OpenStudy (anonymous):
umm 5?
OpenStudy (cwrw238):
right
OpenStudy (cwrw238):
are you getting the idea?
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OpenStudy (anonymous):
kinnda lol i think what would \[\log _{3} 18 \] bee cuz i cant get it
OpenStudy (cwrw238):
here 2 ^x = 18 where x = required log
now this cant solved by inspection as the other 2 could
so you preceed as follows:
ln 2^x = ln 18 where ln is natural log or log to base e
by laws of logs
x ln 2 = ln 18
x = ln 18 / ln 2
which you can do with your calculator
OpenStudy (anonymous):
its 3 tho
OpenStudy (cwrw238):
oh - r us sure its log2 18 not log2 8?
OpenStudy (cwrw238):
because 2^3 = 8
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