SOLUTION: pls help me..!. Question: Express log(ab) + log(sub 100)(a) in terms of u and v if u = log(a^2) and v = log(1/b) . pls pls. answer... thank you..!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: pls help me..!. Question: Express log(ab) + log(sub 100)(a) in terms of u and v if u = log(a^2) and v = log(1/b) . pls pls. answer... thank you..!      Log On


   



Question 937471: pls help me..!.
Question:
Express log(ab) + log(sub 100)(a) in terms of u and v if u = log(a^2) and v = log(1/b) .
pls pls. answer...
thank you..!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express log(ab) + log(sub 100)(a) in terms of u and v if u = log(a^2) and v = log(1/b)
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If you mean logs base 10 and
log%28ab%29+%2B+log%28100%2Ca%29
----
u = log(a^2) --> u = 2log(a)
log(a) = u/2
------
v = log(1/b) --> v = log(1) - log(b) = 0 - log(b)
log(b) = -v
--------
log%28100%2Ca%29+=+log%28a%29%2F2+=+%281%2F2%29log%28a%29
==================================
log(ab) = log(a) + log(b) = u/2 - v
=================
log%28ab%29+%2B+log%28100%2Ca%29+=+u%2F2+-+v+-+u%2F4
= u%2F4+-+v+