anonymous
  • anonymous
Which logarithm is equivalent to log3^16 – log3^2? log332 log314 log38 log318
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
2log₃(x) - 3log₃(y) + log₃(8) Get rid of coefficients: log₃(x²) + log₃(y⁻³) + log₃(8) Now just put it all together by multiplying (since now I have all +'s, notice the NEGATIVE exponent for the y logarithm): log₃(x² * y⁻³ * 8) = log₃(8x² / y³) #17 log₂(64) = ? You need to ask the question (anytime you have a logarithm), the base to the WHAT equals the argument...for instance here the base is 2 and the argument is 64, so: 2 to the WHAT equals 64? The what is what the logarithm evaluates to (exactly like saying 42/6 --> 6 * what = 42, answer 7, therefore 42/6 = 7) So 2*2 = 4, nope 2*2*2 = 8, nope...but what 8² = 64. If 8 = 2*2*2 and 8² = 64, then (2*2*2) * (2*2*2) = 64 = 2⁶ Therefore log₂(64) = 6 Edit: Incidentally, there's no way to "evaluate" a logarithm other than by guess and check...unless you use other numerical techniques...so you need to understand that when you are asked to evaluate a logarithm it will ALWAYS be special. You usually make an educated guess, then verify. For instance, instead of realizing that 8² = 64, we might have just kept multiplying by 2: 2*2 = 4 2*2*2 = 8 2*2*2*2 = 16 2*2*2*2*2 = 32 2*2*2*2*2*2 = 64 1 2 3 4 5 6 --> 2⁶ = 64 Other than that, the only other trick you need to keep in mind is when you have negative answers for the exponent: log₂(1/8) = ? 1/8 = 1/2³ = 2⁻³ Therefore log₂(1/8) = -3 ALSO remember that log(1) = 0, no matter what the base Because any base raised to 0 will ALWAYS equal 1
anonymous
  • anonymous
I think its the 2nd one but i'm not sure
anonymous
  • anonymous
I don't get it

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anonymous
  • anonymous
wait, I'm thinking this is the problem\[\log_3 16 - \log_3 2\]
ganeshie8
  • ganeshie8
Ahh that makes more sense !
anonymous
  • anonymous
when you combine subtracted logs, divide the arguments \[\log_3 a-\log_3b=\log_3 \frac{ a }{ b }\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
so you need to divide 16 by 2
anonymous
  • anonymous
that would equal 8
anonymous
  • anonymous
yes
anonymous
  • anonymous
so the answer would be the 3rd one
anonymous
  • anonymous
looks so. pls give the question the once over when you paste it in. As you can see it causes a lot of confusion trying to guess at the question. You can use the equation tool to make it clearer

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