Question

-38 e^x -2 = -39 + 18 e^x
Find the exact value of x. No decimal entries allowed.

Answer 1

Attempts?

Answer 2

No solution mate

Answer 3

yeah, I just want to know where to start do I combine?

Answer 4

i'm kind of lost on this one.

Answer 5

Just to clarify, it's this, right? \[-38e^x-2=-39+18e^x\]

Answer 6

yes it is

Answer 7

Then start by combining like terms.

Answer 8

e^x= 37/56

Answer 9

Yep. And keep going.

Answer 10

so now ln both sides?

Answer 11

Try it!

Answer 12

Nice, thanks so whenever there is an e we just take the natural log of both sides to get rid of it? which property of logarithms is that?

Answer 13

I got a question lets say for example we were to have 2^x=41 would we do the ln41/ln2 =x ?

Answer 14

\[y=\log_bx \\ b^y=x\]Logarithms and exponents are inverses of each other, so when the two are nested, they cancel.

Answer 15

oh okay, that makes sense I gotta remember the properties exam tomorrow and final next Tuesday.

Answer 16

\[2^x=41\]In this case, you need to take the log(base 2) of both sides:\[\log_2(2^x)=\log_2(41)\]\[x=\log_2(41)=\frac{\log(41)}{\log(2)}\]

Answer 17

why log base 2?

Answer 18

Because log_2 is the inverse of 2^.

Answer 19

It's just like when you have:
\[2x=1\]To isolate x, you perform the INVERSE of the multiplication by 2 (division by 2):\[\frac{2x}{2}=\frac{1}{2}\]It's the same idea, just with logs and powers.

Answer 20

That makes more sense now thanks.