Chapter 5 Questions!!!

[dcc]

since

[Rosie]

Oh, that really helped me. That clarifies everything. Thanks so much

[Glockmeister]

No problem. Do you need help with the other ones too?

[Mao]

Thanks for that. The only thing I dont understand is why 8 becomes log_b(b⁸). Is there a rule for this and does this apply to all logs.

a way to understand this without algebra:

logarithms are by definition, "backwards" exponents, that is:

if , then
or in words, logarithm is finding out how many power you have to raise the base to to get the number

i.e. is asking, in , what does need to be.
this is obviously 3.

so moving back to the problem with 8:

if logarithm of a number is 8, then is the number you have taken the logarithm of,
hence, if the base is b, by definition of logarithms:




I believe your problem lies with you dont exactly understand what logarithms are. they are really just backwards exponentials.

you should be able to work out how they arrived at the logarithm rules once you've come to term with what logarithms are, but here's a few tips:

, because , the power you have looked for is simply, just 1.

, and by expression, that is anything and everything



in a way, the log and power cancel each other out, just like how + and - cancel each other out =)

[Rosie]

Thanks for that explanation. I have a really bad methods teacher this year and I dont understand anything.

[Rosie]

For Q2. log_e(4e^3x) is equal to:

= 3xlog_e(4e)
I'm not sure what to do next?

[ed_saifa]

[Mao]

For Q2. log_e(4e^3x) is equal to:

= 3xlog_e(4e)
I'm not sure what to do next?

the log law is,

in this case, you had , taking 3x out is not correct as you did not consider the 4.

however, if you had , taking 3x out will be correct.

[Rosie]

Could this question be simplified further and if it can't, why not?

[Rosie]

For Q5. log₁₀(5k-3) = 2

= log₁₀(5k-3) = log₁₀10²
Help needed for next step?

[ed_saifa]

Using log laws

[Rosie]

So cont.
10^2 = 5k - 3
103 = 5k
k = 103/5

Yay! Thanks for that log rule

[Mao]

Could this question be simplified further and if it can't, why not?

what we have is:



that is just a plain-simple constant, a number approximately 1.39
to keep it in exact form, we cannot factor out anything else out, and this is its simplest form.

[Rosie]

I just did question 3 and 6 using Mao's log rule he gave to me. These questions become easy when you know which log laws to apply to the question. However, it seems like there are just too many and each question requires a different log law to apply. Is this so?
Thanks also Mao for the explanation on that question i asked about simplifying that question down.

[Mao]

I just did question 3 and 6 using Mao's log rule he gave to me. These questions become easy when you know which log laws to apply to the question. However, it seems like there are just too many and each question requires a different log law to apply. Is this so?
Thanks also Mao for the explanation on that question i asked about simplifying that question down.

no worries =)

you will find that a lot of the later questions require combinations of the log laws, but once you know what to use when, it all becomes algebra hacking and fairly simple to work with.