SOLUTION: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. log (x + 16) = log x + lo

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. log (x + 16) = log x + lo      Log On


   



Question 703915: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.
log (x + 16) = log x + log 16

Found 2 solutions by josgarithmetic, mouk:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Carrying the solution just partway,
log(x+16)=log(x)+log(16), [given]
=log((x)(16)), [property of logarithms]
log(x+16)=log((x)(16))
x+16=16x,
Solve for x.

Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
+log+%28%28x+%2B+16%29%29+=+log+x+%2B+log+16+

Use +logA%2BlogB=logAB+ giving
+log+%28%28x+%2B+16%29+%29=+log+16x+

Use +log+A=log+B++ if and only if +A=B+
+log+%28%28x+%2B+16%29%29+=+log+16x+
+x+%2B+16+=+16x+
+16x+-x+=+16+
+15x+=+16+
+x+=+16%2F15+