Question

How do you solve 30(1.2)^x=45+3x.

Answer 1

Use the Lambert W function.

Answer 2

what is that

Answer 3

hey there:)

Answer 4

have you started anything or completely stuck

Answer 5

haven't started

Answer 6

dont know what to do first

Answer 7

hmm what do you know that can simplify this?

Answer 8

I was thinking first hand to make little clean
\(30(1.2)^x-3x=45 \Longrightarrow 10(1.2)^x-x=15\)

Answer 9

though it does not seem to break to something easier
to solve this we need some other analytical methods

Answer 10

IDK if you learned something of this sort though

Answer 11

algebra alone won't do

Answer 12

I'm smart I can probably understand it

Answer 13

in what course are you given this lol?

Answer 14

algebra 1

Answer 15

You'll need real analysis for this problem it's post calculus usually.

Answer 16

this is a bad question then

Answer 17

are you sure there was an x in the exponent and one that is not?

Answer 18

yes

Answer 19

calculus wont do this either

Answer 20

this is not for alg1 for sure

Answer 21

This foe is beyond you

Answer 22

run

Answer 23

I have a masters in math and I have never studied the things needed to solve stuff like this. There is a thing called "analytic continuation of the product log function"

Answer 24

\(\color{blue}{\text{Originally Posted by}}\) @daniel.ohearn1
Use the Lambert W function.
\(\color{blue}{\text{End of Quote}}\)
I was wondering that this function is about

Answer 25

what*

Answer 26

unless of course this is a special case and there is some trivial solution we are not seeing. But in general....this is not undergraduate math (I don't think).

Answer 27

nevermind

Answer 28

@zzr0ck3r
I'm under gad math
so this cannot be solved with complex?

Answer 29

I am not sure how this is solved.

Answer 30

i think i have the wrong information

Answer 31

oh ok!

Answer 32

could be a trivial solution like you said?

Answer 33

well in general \(a^x=x^b\) is not an easy thing to solve, but some are easy \(2^x=x^2\) has an easy solution 2.

Answer 34

that is what I meant by trivial, but not in this case.

Answer 35

Now I wish I took complex analysis.

Answer 36

yeah seems so, thanks for the clarification :)
I just checked the graph they are two real solutions

Answer 37

isn't it a requirement for a math degree?

Answer 38

there is a solution for every integer

Answer 39

it is not at my school. You just need to take two years of graduate math. I did abstract algebra, topology, graph theory, and a little convex analysis.

Answer 40

No this is not a difficult problem.... Now that I think about it, although it can be solved I imagine with methods of real analysis. For algebra class I would try setting (1.2)^x= (x+15)/10 using your knowledge of graphs and the way they are shaped. At the point of there intersection you will have the solution for x.

Answer 41

There are two intersections amongst the reals.