`log_2(x-4)=6` Solve the equation. Check for extraneous solutions.

To evaluate the given equation `log_2(x-4)=6` , we may apply the logarithm property: `a^(log_a(x))=x` .

Raised both sides by base of `2` .

`2^(log_2(x-4))=2^6`

`x-4=64`

Add `4` on both sides to isolate x.

`x-4+4=64+4`

`x= 68`

Checking: Plug-in `x=68` on `log_2(x-4)=6` .

`log_2(68-4)=?6`

`log_2(64)=?6`

`log_2(2^6)=?6`

`6log_2(2)=?6`

`6*1=?6`

`6=6` TRUE

There is no extraneous solution. The `x=68` is a real solution for the given equation `log_2(x-4)=6` .

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