I've been out of school for years. Went back this semester

They're important for Complexity Theory.

>>8462016
logs turn exponential functions linear and products into sums.

I'm of the opinion, that you should never show an exponential fit plot, but use a log plot and use a linear fit. If that makes sense...going a bit on sleep deprivation at this point.

>>8462016
there are loads of natural phenomena that exhibit exponential or logarithmic behavior with respect to time. google exponential decay for some context

logarithms are used to tune guitars

>>8462016
The big one for e and natural logs is (((interest)))

OP logs are good for finding decay rates of nuclear material, finding interest rates, and some biology stuff (I think).
Just remember that logs allow you to get x out of the exponent slot. They're fun when you get used to working with them.
Also note that calculators will only take logs of base 10 or e( e being an irrational number) so your calculator can't really solve these problems for you.

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>>8462016
>I also thought taking the root of something was the inverse of exponents, teacher is saying this is

Unlike addition and multiplication, exponentiation is not commutative. Ex: 2^3=8 is not 3^2=9 while 2+3=3+2 and 2*3=3*2.

Roots are right inverses and logarithms are left inverses. Ex:
x^3=125 => x=∛125=5
2^x = 64 => x=log_2(64)=6

You use logarithms to find the exponent and roots to find the base.

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>>8462427
>Also note that calculators will only take logs of base 10 or e( e being an irrational number) so your calculator can't really solve these problems for you.

n^log_n(x)=x
log(n^log_n(x))=log(x)
log_n(x)log(n)=log(x)
log_n(x)=log(x)/log(n)

>>8462016
htt ://cims.nyu.edu/~kiryl/Calculus/Section_3.4--Exponential_Growth_and_Decay/Exponential_Growth_and_Decay.pdf

>>8462016
In your context, they find what number you have to raise another number to to get the correct answer. "3 to the *what* will equal 5?" it will be log_3(5).