SOLUTION: log2(x+2)=2+log2(x-2)

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Question 810038: log2(x+2)=2+log2(x-2)



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+2%2C%28x%2B2%29+%29++=+2+%2B+log%28+2%2C+%28x-2%29+%29+
The trick here is to make the substitution
+2+=+log%28+2%2C4+%29+
+log%28+2%2C+%28x%2B2%29+%29++=+log%28+2%2C4+%29+%2B+log%28+2%2C+%28x-2%29+%29+
+log%28+2%2C+%28x%2B2%29+%29+=+log%28+2%2C+%284%2A%28x-2%29%29+%29+
+x+%2B+2+=+4%2A%28+x-2+%29+
+x+%2B+2+=+4x+-+8+
+3x+=+10+
+x+=+10%2F3+
check:
+log%28+2%2C%28x%2B2%29+%29++=+2+%2B+log%28+2%2C+%28x-2%29+%29+
+log%28+2%2C10%2F3%2B2+%29++=+2+%2B+log%28+2%2C+10%2F3-2+%29+
+log%28+2%2C+16%2F3+%29+=+2+%2B+log%28+2%2C+4%2F3+%29+
+log%28+2%2C+5.333+%29+=+2+%2B+log%28+2%2C+1.333+%29+
+2.415+=+2+%2B+.415+ ( approx )
OK