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- anonymous

Which logarithm is equivalent to log3^16 – log3^2?
log332
log314
log38
log318

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- anonymous

Which logarithm is equivalent to log3^16 – log3^2?
log332
log314
log38
log318

- jamiebookeater

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- 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

I think its the 2nd one but i'm not sure

- anonymous

I don't get it

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- anonymous

wait, I'm thinking this is the problem\[\log_3 16 - \log_3 2\]

- ganeshie8

Ahh that makes more sense !

- anonymous

when you combine subtracted logs, divide the arguments
\[\log_3 a-\log_3b=\log_3 \frac{ a }{ b }\]

- anonymous

ok

- anonymous

so you need to divide 16 by 2

- anonymous

that would equal 8

- anonymous

yes

- anonymous

so the answer would be the 3rd one

- 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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