Question 31666
<pre>
Oh this logarithm problems are killing me :)
Can you help! Write hte logarithm of a single expression: 
log[b]6x+4(log[b]x-log[b]y)

(A) log[b] 6x^5/y^4

(B) log [b] 24x^2/y

(C) log [b] 10x/4y

(D) none of these.

Do we even consider the "B" in this expression?

log[b]6x+4(log[b]x-log[b]y)
{{{log (b, (6x)) + 4 (log (b, (x)) - log (b, (y)))}}}
{{{log (b, (6x)) + 4*log (b, (x)) - 4*log (b, (y)))}}} --- Distributing
{{{log (b, (6x)) + log (b, (x)^4) - log (b, (y^4)))}}} ---- Applying {{{c*log (d, (e))}}} = {{{log (d, (e^c))}}}
{{{log (b, ((6x * x^4)/y^4))}}} --- Applying {{{log (c, (d)) + log (c, (e)) = log (c, (d*e))}}} and {{{log (c, (d)) - log (c, (e)) = log (c, (d/e))}}}
{{{highlight(matrix(1,2, log (b, ((6x^5)/y^4)), matrix(1,2, "CHOICE", "(A)")))}}}

Do we even consider the "B" in this expression? 
Don't even consider B or C, as they obviously DO NOT MAKE SENSE. CHOICE D, obviously, is NOT correct either.</pre>