Log problems, help! 3^(2-x) = 5^(x+4), (x^2)(e^(2x)) - e^(2x) = 0

[anna_pilk]

I have a paperwork with a ton of log problems on it, and there are two difficult ones I cannot seem to get.

3^2-x=5^x+4
The question gives a hint saying to log both sides and solve for x, which I have done, but none of my answers check. How would you set this up?

x²e^2x-e^2x=0

This one says to factor and set the factors equal to 0, but I can't get it to work either.

 

[Ishuda]

I have a paperwork with a ton of log problems on it, and there are two difficult ones I cannot seem to get.

3^2-x=5^x+4
The question gives a hint saying to log both sides and solve for x, which I have done, but none of my answers check. How would you set this up?

x²e^2x-e^2x=0

This one says to factor and set the factors equal to 0, but I can't get it to work either.

For the first, what did you get when you took the log of both sides?

For the second
x²e^2x-e^2x = e^2x(x²-1) = 0
so at least one of those factors must be zero. Can e^2x ever be zero? How would you factor x²-1?

 

[stapel]

1. 3^2-x=5^x+4

The question gives a hint saying to log both sides and solve for x, which I have done, but none of my answers check.

What were your steps? What were your answers?

How would you set this up?

I would "set this up" (that is, I would start my work) in exactly the manner suggested: by taking logs of either side of the equation.

2. x²e^2x-e^2x=0

This one says to factor and set the factors equal to 0, but I can't get it to work either.

What was your factorization? Once you noted that the one factor could never equal zero, what did you conclude?

Please be complete. Thank you!