Can #5x^4=3^x# be solved algebraically?

Question

I solved a problem similar to this using graphing but are there algebra techniques for solving an equation of this form?

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Answer 1 · 2017-01-10T02:21:40

With powers, the remedy is often logaritms.

Use:
#log(A*B)=logA+logB# and #logA^B=BlogA#

#log(5x^4)=log(3^x)->#
#log5+4logx=xlog3->#

#color(red)(log5=xlog3-4logx)#

#color(red)(log5=log3^x-logx^4)#

#color(red)(log5=log(3^x/x^4)#

and now I'm just going in circles