x^5 = g^x

Been a minute since I’ve had to do anything like that, so the best I can do is say that the solution probably involves using logs.

Jason

x = 1; when g = 1

I last studied math nearly 60 years ago.......stopped taking math classes as those classes had become irrelevant to me and my every day life.......I was no longer able to make the connection with those courses and my world.......so, I stopped.
But, I was well grounded in basic math.......even taught math for awhile with adult students who had also lost their connection and understanding of basic math......it was always fun watching a light bulb go on when they got it......because I had explained it in terms they related to and understood.

To give you a better answer, what is g??...... a constant or a variable.......that would be the difference between basic math and more advanced math.

Roger has shown one special case: when x=1, g also equals 1.
Here are a couple of other special cases:
Let x=2.  Then 2^5=32.  So we have 32=g^2 and g must equal sqrt32 = 4sqrt2.

Let x=1/2.  Then (1/2)^5=1/(2^5)=1/32.  So we have 1/(2^5)=g^(1/2) and g must equal 1/(2^10) =1/1024.

If you have a pocket calculator that has a sqrt function, it is possible to solve this when x is 2 raised to a power.

I found this but had a hard time following it.
https://youtu.be/LESu08vVvrQ?si=RR4fwjJifCnv3iQO

In the video, what I thought was the letter g is being treated as the number 9.......either way, the video makes my point about math getting to a place that is difficult to relate to real life situations........I sort of felt that math was a way of looking at situations in life and summarizing that situation in numbers......then applying a logical way of making a deduction with numbers to arrive at a conclusion of what any practical situation we faced called for.......like asking what is the probability of getting with a young woman who is a billionaire....... has more men than the US Army........and does not know you exist??