Solve the equation : 8^2x-1 = 16^x+1

Question

i know you have to log both sides

log8^2x-1 = log16^x+1

and then you use the exponential rule

2x-1 log8 = x+1 log16

but then i don't know what to do...

Answer 1

Your steps are correct if the equation was:
8^(2x-1) = 16^(x+1)
and assuming this is the case.

Since 8=2^3, and 16=2^4,
you can simplify further using the same rule of logarithms:
log(a^b)=b×log(a)