Solve for m...  -2log2(-8m-1)=0

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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` .

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