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OpenStudy (anonymous):
OpenStudy (anonymous):
fill in the blank
\[2^{blank}=64\]
OpenStudy (anonymous):
6
OpenStudy (anonymous):
got the first one!
OpenStudy (anonymous):
\[64^{blank}=2\] this one is trickier
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OpenStudy (anonymous):
yeaa... ummmm
OpenStudy (anonymous):
hint, how do you write "sixth root" as an exponent?
that is how you you write
\[\sqrt[6]{64}=2\] using exponential notation?
OpenStudy (anonymous):
1/6
OpenStudy (anonymous):
ok two down!
OpenStudy (anonymous):
:]
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OpenStudy (anonymous):
\[81^{blank}=\frac{1}{3}\] another tricky one
OpenStudy (anonymous):
hint: first take the fourth root, then take the reciprocal
OpenStudy (anonymous):
ok
OpenStudy (anonymous):
81^1/4
OpenStudy (anonymous):
3=1/3
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OpenStudy (anonymous):
that will get you from 81 to 3
to get to \(\frac{1}{3}\) write
\[81^{-\frac{1}{4}}=\frac{1}{3}\]so answer to third one is
\[\log_{81}(\frac{1}{3})=-\frac{1}{4}\]
OpenStudy (anonymous):
then negative exponent means take the reciprocal
OpenStudy (anonymous):
ohh okay got it!!
OpenStudy (anonymous):
good because you are going to need it for the next one too!
OpenStudy (anonymous):
yea im trying!
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OpenStudy (anonymous):
\[(\frac{1}{3})^{blank}=27\]
OpenStudy (anonymous):
flip it, then cube it
OpenStudy (anonymous):
-3
OpenStudy (anonymous):
ok! got it! one more to go
OpenStudy (anonymous):
its hard..!
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OpenStudy (anonymous):
maybe better to rewrite as
\[\log_2(\sqrt{2})-\log_2(4)\] the second one is easy
OpenStudy (anonymous):
ohh yea division rule..
OpenStudy (anonymous):
yea its 2
OpenStudy (anonymous):
ohh the first one is 2^(1/2)
OpenStudy (anonymous):
so 2^(1/2)-2
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OpenStudy (anonymous):
last one??
OpenStudy (apoorvk):
This is a perfect example of a tutoring!! All hail @satellite73 !!