Mathematics
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OpenStudy (anonymous):
can any one solve this?(log(a)(x^3))+(log(a)(sqrtx))=
answer has to be in klog(a)x form
thanks already :)
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OpenStudy (amistre64):
is that base a?
OpenStudy (amistre64):
log[a](x^3) like this?
OpenStudy (amistre64):
3loga(x) + (1/2)loga(x)
OpenStudy (amistre64):
loga(x)(3+(1/2)) ??
OpenStudy (anonymous):
Amistre, I think contact has been lost lol.
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OpenStudy (amistre64):
looks right lol
(6/2) loga (x)
OpenStudy (amistre64):
:) but the math remains lol
OpenStudy (anonymous):
Hahahaa, so very true!
OpenStudy (amistre64):
(7/2) loga(x)
OpenStudy (anonymous):
yes a is the base, soz my internet played up :S
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OpenStudy (amistre64):
can we factor out the loga(x) like that tho?
OpenStudy (anonymous):
\[\log_{a} x^3+\log_{a} sqrtx\]
OpenStudy (amistre64):
if we multiply it togeter again we get:
loga[sqrt(x^7)] so its good
OpenStudy (amistre64):
(7/2) loga(x) is your answer
OpenStudy (anonymous):
where did 7 come from?
soz but i dont get the stuff you lot did at the top :S
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OpenStudy (amistre64):
3 + 1/2 = 3' 1/2 to get it into an improper fraction (topheavy) we multiply 3 by the denom and add the numerator;
3(2) = 6 + 1 = 7.... 7/2
OpenStudy (amistre64):
OR we could go the route of changing addition of logs back into multiplication of logs
OpenStudy (anonymous):
ok :)
multiplication logs?
OpenStudy (amistre64):
loga(x^3 sqrt(x)) = loga(sqrt(x^7)) = loga(x^(7/2))
(7/2) loga(x)
OpenStudy (amistre64):
loga(x) + loga(y) = loga(xy)
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OpenStudy (amistre64):
loga(x^n) = n loga(x) as well
OpenStudy (anonymous):
ok
so 7/2logax is the answer right?
OpenStudy (amistre64):
yes; (7/2) loga(x) is the answer
OpenStudy (anonymous):
\[7/2\log_{a} x\]
OpenStudy (anonymous):
yay!
ill give u all medals :)
thx
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OpenStudy (amistre64):
im gonna need a new cigar box to keep these things in ;)
OpenStudy (anonymous):
:p