Solving Another Challenging Exponential Equation

[@firelow]

Hearing this "Hello, everyone" makes my mind shift into math mode. I'm being Pavlov trained.

[@mcwulf25]

What I like about this is that it's easy to see the x=2 solution, but work is required to extract the other solution.
I always try and work these out in my head, but this was too much 😅. Thanks!!!

[@neuralwarp]

We've done lots of those. Can we do loop integrals, partial differential equations, quaternions, n-dimensional manifolds, or boolean logic now?

[@JayPaulson-hg2mc]

You skipped the naive method, which in this case was probably best. 100 is 5^2*2^2 and one of the multiplicants on the left is 5^x so try x=2. That works. So then do the log to find the other solutions and realize that x=2 has to be one of the factors and synthetic division will give you the other.

[@RobG1729]

Have I had enough coffee this morning?
Let's watch a SyberMath video and find out.

[@honestadministrator]

2 ^ (3x /(x+1) -2) times 5 ^(x-2) = 1
This consists of two different equations
3x/(x+1) = 2
And x = 2
Both of them are consistent and leads to x= 2

[@kaaehtla]

very short solution: 8^(x/x+1).5^x= 25*4= (5^2)(2^2)
2^3(x/x+1).5^x= (5^2)(2^2)
so x=2 and 2^3(x/x+1)= 2 hence x=2

[@ZipplyZane]

9:27 reverse cross multiplication. I guess we can call it "uncross division"?

[@popitripodi573]

Very nice!!!! I liked it! I used the first method to solve it

[@antenym8947]

There is an easy way of solving these in general by doing e^(ln(8)*x/(x+1)+ln(5)x)=e^ln(100) and then the rest is very obvious.

[@mehrdadbasiri9968]

Fantastic question...👌👌👌.

[@carly09et]

x=2 is the first solution. I can use log to get an 'ugly' solution

[@mathswan1607]

x=2 or x=-1/log5

[@scottleung9587]

Nice!

[@rakenzarnsworld2]

4*25=100
x = 2

[@lori2364]

👏

[@kaushikbasu9707]

2

[@broytingaravsol]

x=2, -1/log5

[@yuvanmar42]

-1 is invalid cause you get -1/0

[@broytingaravsol]

@@yuvanmar42 what??

[@krishnamoyghosh6047]

X=2 but nice problem

[@KennethChile]

But that's only one solution. Do the math to obtain the other one.

[@mcwulf25]

Is that your final answer?

[@krishnamoyghosh6047]

@@mcwulf25 no no there are two solution. I worked out the 1st answer mentally.