SOLUTION: log4 square root x+3 = 1/4 + log4 square root 2x-1

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Question 1029314: log4 square root x+3 = 1/4 + log4 square root 2x-1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+4%2Csqrt%28+x%2B3+%29%29+=+1%2F4+%2B+log%28+4%2Csqrt%28+2x-1+%29+%29+
+log%28+4%2Csqrt%28+x%2B3+%29%29+-++log%28+4%2Csqrt%28+2x-1+%29+%29+=++1%2F4++
+log%28+4%2C+sqrt%28+%28x%2B3%29%2F%282x-1%29+%29%29+=+1%2F4+
+%281%2F2%29%2Alog%28+4%2C++%28x%2B3%29%2F%282x-1%29+%29+=+1%2F4+
+log%28+4%2C++%28x%2B3%29%2F%282x-1%29+%29+=+1%2F2+
+log%28+4%2C++%28x%2B3%29%2F%282x-1%29+%29+=+log%28+4%2C+2+%29+
+%28+x+%2B+3+%29+%2F+%28+2x+-+1+%29+=+2+
+x+%2B+3+=+2%2A%28+2x+-+1+%29+
+x+%2B+3+=+4x+-+2+
+3x+=+5+
+x+=+5%2F3+
--------------------
check answer:
+log%28+4%2Csqrt%28+x%2B3+%29%29+=+1%2F4+%2B+log%28+4%2Csqrt%28+2x-1+%29+%29+

+log%28+4%2Csqrt%28+14%2F3+%29%29+=+1%2F4+%2B+log%28+4%2Csqrt%28+7%2F3+%29+%29+
+%281%2F2%29%2Alog%28+4%2C+14%2F3+%29+-+%281%2F2%29%2Alog%28+4%2C+7%2F3+%29+=+1%2F4+
+%281%2F2%29%2A%28+log%28+4%2C+14%2F3+%29+-+log%28+4%2C+7%2F3+%29+%29+=+1%2F4+
+log%28+4%2C+14%2F3+%29+-+log%28+4%2C+7%2F3+%29+=+1%2F2+
+log%28+4%2C+14%2F3+%29+-+log%28+4%2C+7%2F3+%29+=+log%28+4%2C2+%29+
+log%28+4%2C+%28+%28+14%2F3%29%2F%28+7%2F3%29+%29+%29+=+log%28+4%2C2+%29+
+14%2F7+=+2+
+2=+2+
OK
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It is also true that
+log%28+4%2C++%28x%2B3%29%2F%282x-1%29+%29+=+1%2F2+
+log%28+4%2C++%28x%2B3%29%2F%282x-1%29+%29+=+log%28+4%2C+-2+%29+
You can figure that out ( if there is an answer )
Hope this helps