Question

( log _{2}left(4^{x}+4right)=log _{2}left(2^{2 x+1}-3.2^{x}right) )
( 4^{x}+4=2^{2 x} cdot(2)-3left(2^{x}right) )
( 2^{2 x}+4=2^{2 x}(2)-3left(2^{x}right) )
( 0=2^{2 x}-3left(2^{x}right)-4 )
( therefore quad ) Lit ( 2^{x}=t )
( t^{2}-3 t-4=0 )
( t=-1,4 )
( 2^{x} eq-1 quad ) &o ( quad 2^{x}=4 )
( x=2 )

# 38. log, (4* + 4) = log 2* + log; (2X+1 – 3)

Solution