Question

Can someone explain inverse trig functions?

Answer 1

Here is a screenshot of my practice questions. Problem is, I'm not quite sure what it's asking. It's not graded but I'd still like to know how to do them.

Answer 2

These are not trig functions :)
Having a little trouble understanding the relationship between exponentials and logs though?

Answer 3

I meant inverse log functions :) and yes

Answer 4

Only the last two problems require us to know anything about inverses.
The first 4 problems are just some simple log rules.

Answer 5

Recall the exponent log rule,
\(\large\rm log(a^b)=b\cdot log(a)\)
Do you see how we can Abbly this rule to the first question?

Answer 6

The first one would be 5 log 10 then?

Answer 7

I was thinking it had something to do with inverse functions since that was what the lesson was about.. mind explaining the last two?

Answer 8

Good.
And from there we can use another property of logs:
When the `base` of the log is the same as the `contents` of the log,
then the result is 1.

Examples:
\(\large\rm log_2(2)=1,\qquad\qquad log_7(7)=1\qquad\qquad ln(e)=1\)

Answer 9

And recall that when your log has no subscript,
it defaults to a 10, ya?

Answer 10

So we have \(\large\rm 5\cdot log_{10}(10)\)

Answer 11

Ya :)

Which is 5, correct?

Answer 12

yay

Answer 13

So um, recall that `division` is the inverse of `multiplication`.
If you have something like 7x, and you divide that expression by 7,
The multiplication and division sort of "undo" one another, ya?
And we're left with no multiplication or division, just x.

Answer 14

Right.

Answer 15

In the same way, `exponentiation` and `logarithm` are inverses of one another.

So here is a weird looking example.
If I have an expression \(\large\rm \log_2(x)\) and I apply exponentiation,
\(\large\rm 2^{log_2(x)}\) then the exponential base and the log will "undo" one another just as we would expect inverses to do, leaving us with \(\large\rm x\).