SOLUTION: Given that {{{u=log(base9)x}}}, FIND IN TERMS OF U, {{{log(base2)81}}} *PLEASE ANSWER AS SOON AS POSSIBLE BRO!!!!!! :) =) BTW, you are supposed to somehow express {{{log(ba

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given that {{{u=log(base9)x}}}, FIND IN TERMS OF U, {{{log(base2)81}}} *PLEASE ANSWER AS SOON AS POSSIBLE BRO!!!!!! :) =) BTW, you are supposed to somehow express {{{log(ba      Log On


   



Question 467239: Given that u=log%28base9%29x, FIND IN TERMS OF U,
log%28base2%2981


*PLEASE ANSWER AS SOON AS POSSIBLE BRO!!!!!! :) =) BTW, you are supposed to somehow express log%28base2%2981 in terms of u, and not solve it with a calulator. :)

Found 2 solutions by Big Poop, josmiceli:
Answer by Big Poop(157) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
given:
+u+=+log%289%2Cx%29+
(1) +9%5Eu+=+x+
I will say that:
+v+=+log%282%2C81%29+
+2%5Ev+=+81+
(2) +2%5Ev+=+9%5E2+
Now the problem is to find v in terms of u
I will take the vth root of both sides of (2)
(2) +%282%5Ev%29%5E%281%2Fv%29+=+%289%5E2%29%5E%281%2Fv%29+
(2) +2+=+9%5E%282%2Fv%29+
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Now I will raise each side of (2) to the +%28u%2Av%29%2F2+ power
(2) 2%5E%28%28u%2Av%29%2F2%29+=+9%5Eu+
but,
(1) +9%5Eu+=+x+
so,
+x+=+2%5E%28%28u%2Av%29%2F2%29+
take log base 2 of both sides
+log%282%2Cx%29+=+%28u%2Av%29%2F2+
+u%2Av+=+2%2Alog%282%2Cx%29+
+v+=+%282%2Alog%282%2Cx%29%29+%2F+u+
+log%282%2C81%29+=+%282%2Alog%282%2Cx%29%29+%2F+u+
This is the best I can do, because if I do the
substitution +x+=+9%5Eu+, then u just
gets eliminated from the equation.
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check answer using my Casio fx-115ES
I'll pick any value for x, like +x+=+13+
(1) +9%5Eu+=+x+
(1) +9%5Eu+=+13+
Take log base 9 of both sides
(1) u+=+log%289%2C13+%29
(1) u+=+1.16736+
and
+log%282%2C81%29+=+6.33985+
so
+log%282%2C81%29+=+%282%2Alog%282%2Cx%29%29+%2F+log%289%2Cx%29+
+log%282%2C81%29+=+%282%2Alog%282%2Cx%29%29+%2F+log%289%2Cx%29+
+6.33985+=+%282%2Alog%282%2C13%29%29+%2F+log%289%2C13%29+
+6.33985+=+7.40088+%2F+1.16736+
+6.33985+=+6.33984+ close enough