Michael J. answered • 05/22/15
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Effective High School STEM Tutor & CUNY Math Peer Leader
We have a difference in logs. We can rewrite this as a quotient.
log2(x / (3x + 5)) = 4
The solution to a logarithm is the exponent of the log's base.
24 = x / (3x + 5)
16 = x / (3x + 5)
Multiply both sides of equation by (3x + 5).
16(3x + 5) = x
48x + 80 = x
Subtract 48x on both sides of equation.
80 = -47x
Divide both sides of equation by -47.
-80/47 = x
Andrew M.
The first term in the original equation is only undefined until you apply the rules of logarithms to combine the equation...
the answer is not log2(-80/47)...
It's log2((-80/47)/(3(-80/47)+5))=4
Since 24=16 the answer is correct if
(-80/47)/(3(-80/47)+5=16
so let's see...
(-80/47)/(-240/47 +5) = 16
(-80/47)/(-5/47) = 16
(-80/47)(-47/5)=16
16=16
The answer x=-80/47 is correct
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05/23/15
Mark M.
05/22/15