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log a^x = x log a

can be true. Can someone help me?

Another question deals with an application of it which made me really confused:

Factorise (4a^3) - (29 a^2) + 47a - 10

then solve (4*4^3x) - (29*4^2x) + 47*4^x - 10 = 0

I see many similarities between the two equations, but I dunno how to factorise polynomials. Plz help me!