Log2(x-3)² + 24 >(log2(x-3))²
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let see here
log2(x-3)² + 24 >(log2(x-3))²
2log(x-3) + 24 > (log2(x-3))²
now suppose log2(x-3)= a
then
2a +24>a²
a²-2a-24<0
We know that this is quadratic equation and condition is
a<0. and D>0
log2(x-3)<0 and 4a²+96<0
x-3<1 and a²+24<0
x<4 and this is not possible
so x<4
log2(x-3)² + 24 >(log2(x-3))²
2log(x-3) + 24 > (log2(x-3))²
now suppose log2(x-3)= a
then
2a +24>a²
a²-2a-24<0
We know that this is quadratic equation and condition is
a<0. and D>0
log2(x-3)<0 and 4a²+96<0
x-3<1 and a²+24<0
x<4 and this is not possible
so x<4
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