Solve log2 x5 log4 x1 Solutionlog2x5 log4x1 log2x5 log22x1

Solve log_2 (x-5) = log_4 (x+1)

log₂(x-5) =log₄(x+1)

log₂(x-5) =log_2²(x+1)

log_a^bc =(1/b)log_ac

log₂(x-5) =(1/2)log₂ (x+1)

multiply by 2 on both sides

2log₂(x-5) =log₂ (x+1)

a log_bc =log_bc^a

log₂(x-5)² =log₂ (x+1)

=>(x-5)² =(x+1)

=>x²-10x+25=x+1

=>x²-10x-x+25-1=0

=>x²-11x+24=0

=>x²-8x-3x+24=0

=>x(x-8)-3(x-8)=0

=>(x-3)(x-8)=0

=>x=3,x=8

but x has to be grater than 5 as domain of log₂(x-5) is x >5

so x =8 is the answer