Help me solve this logarithm question

I checked the answer and it says



I don't really understand this.
Can anyone explain this to me? I couldn't find any online videos to help me understand this either.

I do know how to convert from index form to logarithmic form and simplify logarithmic expressions, solve some logarithmic equations. I don't get how to sketch the graph to find the answer in these 2 questions though.

 

Sketch y_1 = log(x). On the same axis system, sketch y_2 = 5 - x. Find where the two lines intersect.

 

If you want a more "analytic" (non-"sketch") take the exponential of both sides:
x= e^{5- x}= e^5e^{-x}
Multiply both sides by e^x:
xe^x= e^5.

Apply the "Lambert W" function (defined as the inverse function to xe^x) to both sides:
x= W(e^5).