SOLUTION: hello. we are learning about properties of logarithms. we were asked to solve these equations. {{{ log ( 4, a ) + log ( 4, 9 ) = log ( 4, 27 )}}} and {{{ log ( 2, y+2 ) - log ( 2,

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: hello. we are learning about properties of logarithms. we were asked to solve these equations. {{{ log ( 4, a ) + log ( 4, 9 ) = log ( 4, 27 )}}} and {{{ log ( 2, y+2 ) - log ( 2,       Log On


   



Question 436746: hello. we are learning about properties of logarithms. we were asked to solve these equations. +log+%28+4%2C+a+%29+%2B+log+%28+4%2C+9+%29+=+log+%28+4%2C+27+%29 and +log+%28+2%2C+y%2B2+%29+-+log+%28+2%2C+y-2+%29+=+1+ thank you very much.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log+%28+4%2C+a+%29+%2B+log+%28+4%2C+9+%29+=+log+%28+4%2C+27+%29
+log%284%2C+9a%29+=+log%284%2C27%29+
+9a+=+27+
+a+=+3+
--------
+log+%28+2%2C+y%2B2+%29+-+log+%28+2%2C+y-2+%29+=+1+
Note that +log%282%2C2%29+=+1
+log%282%2Cy%2B2%29+=+log%282%2Cy-2%29+%2B+log%282%2C2%29+
+log%282%2Cy%2B2%29+=+log%282%2C2%2A%28y-2%29%29+
+y+%2B+2+=+2%2A%28y-2%29+
+y+%2B+2+=+2y+-+4+
+y+=+6+
check answer:
+log+%28+2%2C+y%2B2+%29+-+log+%28+2%2C+y-2+%29+=+1+
+log+%28+2%2C+6%2B2+%29+-+log+%28+2%2C+6-2+%29+=+1+
+log+%28+2%2C+8+%29+-+log+%28+2%2C+4+%29+=+1+
+log+%28+2%2C+2%5E3+%29+-+log+%28+2%2C+2%5E2+%29+=+1+
+3+-+2+=+1+
+1+=1+
OK