5^x=3^x+2 solve equation express irrational solutions in exact form

Question

radar · Answer

x=1

radar · Answer

From inspection.  Now how to solve step by step!

anonymous · Answer

i need to solve step by step that is were i am confused

radar · Answer

Using logs would end up with decimal values, and the want "exact form"

radar · Answer

@tiaph, any ideas?

radar · Answer

It is above my paygrade cassyynn.  Maybe repost it and see if the big dogs will bite it lol.

anonymous · Answer

thanks for trying

radar · Answer

Sorry I did not solve it.  I am going to have to review exponential equations!

anonymous · Answer

can be written as 2=5^x-3^x. 5^x-3^x... same exponents... so reduce to 2=2^x. x=1 because any other real value of x would make the equation not solvable.

anonymous · Answer

but if you put 1 back in for 2 it doesn't make a real answer

radar · Answer

But you don't do that....you only substitute the 1 for x$$5^{1}=3^{1}+2$$
5=5

radar · Answer

@mariamjones, are you sure:$$5^{x}-3^{x}=2$$ Lets say would $$2^{x}+4^{x}=72$$
$$6^{x}=72$$  I don't think so.  In this case x=3.  Think about this.