Solve for x and check: 16^x = 8^x-1

Question

This question not only has to be solved but has to be checked to make sure there are no mistakes with the computations.

Answer 1

???????????????? is that spozed tu be 8^(x-1) ??????????????????

16^x =8^(x-1)

log(16^x)=x*log(16) =log[8^(x-1)]=(x-1)*log(8)

x*log(16)=(x-1)*log(8)

x/(x-1)=log(8)/log(16)=0.903089987 / 1.204119983

=0.749999999 or maebee=0.75

x=0.75(x-1)=0.75x -0.75

0.25x=-0.75

x=-3

####### 16^-3=1/16^3=1/4096=0.000244140625

x-1=-4 & 8^-4=1/8^4=1/4096