Question 937471
 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(ab) + log(100,a)}}}
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u = log(a^2) --> u = 2log(a)
log(a) = u/2
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v = log(1/b) --> v = log(1) - log(b) = 0 - log(b)
log(b) = -v
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{{{log(100,a) = log(a)/2 = (1/2)log(a)}}}
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log(ab) = log(a) + log(b) = u/2 - v
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{{{log(ab) + log(100,a) = u/2 - v - u/4}}}
= {{{u/4 - v }}}