In order to solve this equation for m, we need to use the logarithmic rules to get m to be on one side of the equation and everything else on the other side:

`-2log_2(-8m-1)=0` use power rule

`log_2(-8m-1)^{-2}=0` switch to exponential form

`(-8m-1)^{-2}=2^0` simplify each side

`1/(-8m-1)^2=1` cross-multiply

`1=(-8m-1)^2` simplify inside brackets (since squared)

`1=(8m+1)^2` take square roots of each side

`+-1=8m+1` simplify

`+-1-1=8m` divide

`m=0` or `m=-1/4`

Now sub back into the original equation and we see that m=0 is not a valid solution.

**The solution to the equation is `m=-1/4` .**