Question

I really don't understand logarithms and my pre-cal final is on Thursday. Can someone help explain them to me?

Answer 1

what don't you understand specifically ?

Answer 2

it helps if you think of them as exponents. what kind of problems are you expected to do?

Answer 3

solving trigonometric equations for one. I can do the simple problems, like rewriting in exponential form though I struggle. But I have a hard time with a long equation.

Answer 4

Logs are the inverses of exponential functions in the form \[\log_{a}x \]

Answer 5

confused. is it logs or trig?

Answer 6

give us an example

Answer 7

remember that
\[b^x=y\iff \log_b(y)=x\] so for example
\[2^x=10\iff \log_2(10)=x\]

Answer 8

Oh, I'm so sorry. I mean logarithmic equations. I'm studying trigonometric identities too, I'm sorry.
But an example would be log(base 8) (x^2 +11) = log(base 8) 92

Answer 9

if the bases are the same, as they are in this question, then the inputs must be the same as well. so this really has very little to do with logs. solve
\[x^2+11=91\]

Answer 10

typo there i meant solve
\[x^2+11=92\]

Answer 11

so, you can just cancel the logs and just solve like a normal equation?

Answer 12

As long as they are of the same base.

Answer 13

yes but it your anser has to be >1

Answer 14

it is not exactly "canceling" but logs are one to one functions, so if
\[\log_b(x)=\log_b(y)\implies x = y\]

Answer 15

I have yet to see one in my precal class where they aren't the same base. I don't think she would put that on the final, but who knows. If I come across a problem where they don't have the same base, what do I do?

Answer 16

and as eherre said, make sure to only write the positive answer, because you cannot take the log of a negative number

Answer 17

what about natural logs? For example, ln(3x^2-4) +ln(x^2 +1) = (2-x^2) ?

Answer 18

if the bases are different you can use the "change of base formula" which says
\[\log_a(x)=\frac{\log_b(x)}{\log_b(a)}\] which also means you can solve
\[2^x=10\] by
\[x=\frac{\log(10)}{\log(2)}\]

Answer 19

okay, I understand you.
What about condensing and expanding?
I have done okay with the majority of those, but I have problems with the ones that have exponents.

Answer 20

go to www.patrickjmt.com and he has a lot of helpful video tutorials