How do you call this math in english?

[woutR]

I'm searching for some math help online, but I don't know how this is called in English. (Dutch stuff wasn't helpful enough)

The chapter is called 'Exponential growth' (roughly translated) and I don't think it's too hard, I'm just missing some ground rules or tricks. Of course I've already checked Exponential Growth on google, but the stuff was too basic, mostly with just starting capital that grows over time.

So this is what it looks like

Give exact notations of the following:
7 x 8^t = 224
the answer is supposed to be t = 1(2/3)

8^t = 32
(2^3)t = 32 so 2^3t = 2^5

And then later I gotta work with 'log'. Calculate without the help of a calculator
^3log 27
^2log (1/16)

I remember some time ago someone posted a youtube channel with loads of math help going from algebra to whatever, really had everything. Anyone remember the name of that channel?
The answers are from my answers book, I don't really know how to calculate this stuff. I've been a real lazy student so now it's time to pick up the slack.
Any help would be appreciated.

[BloodyBlade]

I'm searching for some math help online, but I don't know how this is called in English. (Dutch stuff wasn't helpful enough)

The chapter is called 'Exponential growth' (roughly translated) and I don't think it's too hard, I'm just missing some ground rules or tricks. Of course I've already checked Exponential Growth on google, but the stuff was too basic, mostly with just starting capital that grows over time.

So this is what it looks like

Give exact notations of the following:
7 x 8^t = 224
the answer is supposed to be t = 1(2/3)

8^t = 32
(2^3)t = 32 so 2^3t = 2^5

And then later I gotta work with 'log'. Calculate without the help of a calculator

^2log (1/16)

I remember some time ago someone posted a youtube channel with loads of math help going from algebra to whatever, really had everything. Anyone remember the name of that channel?
The answers are from my answers book, I don't really know how to calculate this stuff. I've been a real lazy student so now it's time to pick up the slack.
Any help would be appreciated.

^3log 27 = 9 I guess, it's been a while since I've done maths tho

[woutR]

ok I just realized this is a failed question since I don't even know how to word this subject in Dutch.
You can show off mad math skills and help me now, please.

[Jaapii]

first one is easy
you gotta do log of both of them
so log(7x8^t) = log(224)
and log(axb) = loga + logb so log7 + log8^t = log224
you can place the ^t in front so it becomes log7 + txlog8 = log224
so (log224 - log7)/log8 is the correct answer which is 5/3, right? I hope you can use ur calculator for that last thing.

³log27 means that 3^x = 27 and you gotta find the x, now make 27, 3^3 and voila, you have your answer, 3.
same for ²log(1/16), 2^x = 1/16, make 1/16 with 2^.., 1/16 = 16^-1 and 16 = 2^4 so 1/16 = 2^-4
so the x = -4 here.

I hope I helped you out a bit, altho I think the last explanation is a bit technical luls

[woutR]

³log27 means that 3^x = 27 and you gotta find the x, now make 24, 3^3 and voila, you have your answer, 3.

I get that 3^3=27, but where does this 24 come in?

[evilpeta]

typo

[Azilius]

I just finished logarithms in math. The most helpful thing is to know the few 'rules'

Wiki has them listed nicely.
http://en.wikipedia.org/wiki/Logarithm

Go to 'properties'

log(x*y) = logx + logy
log(x/y) = logx - logy
Log(x^y) = ylog(x)

Few others. Once you know the base rules all of logarithms should come naturally.