Hi I need help on how to do this exponent problem thanks.

Question

solve for x:

4^2013 - 4^2012 - 4^2011 + 4^2010 = 45(2^x)

Answer 1

Don't get scared by the appearance of the question!

Factorize the common factor 4²⁰¹⁰:
4^2013 - 4^2012 - 4^2011 + 4^2010
=(4³-4²-4+1)*4²⁰¹⁰
=(64-16-4+1)*4²⁰¹⁰
=45*4²⁰¹⁰
=45*(2²)²⁰¹⁰
=45*2⁴⁰²⁰
By inspection, x=4020.