SOLUTION: Solve for x show work 1. Log5(x+2)=1 - Log5(x+6) 2. Log2(x+7)=2 + Log2(x+4)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x show work 1. Log5(x+2)=1 - Log5(x+6) 2. Log2(x+7)=2 + Log2(x+4)       Log On


   

Question 1149864: Solve for x show work
1. Log5(x+2)=1 - Log5(x+6)
2. Log2(x+7)=2 + Log2(x+4)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +log%28+5%2C+%28x%2B2%29+%29+=+1+-+log%28+5%2C+%28+x%2B6+%29+%29+
(1) +log%28+5%2C+%28x%2B2%29+%29+=+log%28+5%2C5+%29+-+log%28+5%2C+%28+x%2B6+%29+%29+
(1) +log%28+5%2C+%28x%2B2%29+%29+=+log%28+5%2C+%28+5%2F%28+x%2B6+%29%29+%29+
(1) +x+%2B+2+=+5%2F%28+x%2B6+%29+
(1) +%28+x%2B2+%29%2A%28+x%2B6+%29+=+5+
(1) +x%5E2+%2B+8x+%2B+12+=+5+
(1) +x%5E2+%2B+8x+%2B+7+=+0+
(1) +%28+x+%2B+7+%29%2A%28+x+%2B+1+%29+=+0+
+x+=+-7+
+x+=+-1+
-----------------
check answer:
(1) +log%28+5%2C+%28x%2B2%29+%29+=+1+-+log%28+5%2C+%28+x%2B6+%29+%29+
(1) +log%28+5%2C+%28-1%2B2%29+%29+=+1+-+log%28+5%2C+%28+-1%2B6+%29+%29+
(1) +log%28+5%2C+1+%29+=+1+-+log%28+5%2C+5+%29+
(1) +0+=+1+-+1+
OK
Note that +x+=+-7+ does not work because
it gives you:
(1) +log%28+5%2C+%28-7%2B2%29+%29+=+1+-+log%28+5%2C+%28+-7%2B6+%29+%29+
There is no log to a positive base that gives a
negative result
===========================================
(2) +log%28+2%2C+%28x%2B7%29+%29+=+2+%2B+log%28+2%2C+%28x%2B4%29+%29+
(2) +log%28+2%2C+%28x%2B7%29+%29+=+log%28+2%2C+4+%29+%2B+log%28+2%2C+%28x%2B4%29+%29+
(2) +log%28+2%2C+%28x%2B7%29+%29+=+log%28+2%2C+4%2A%28+x%2B4+%29+%29+
(2) +x+%2B+7+=+4%2A%28+x%2B4+%29+
(2) +x+%2B+7+=+4x+%2B+16+
(2) +3x+=+-9+
(2) +x+=+-3+
----------------------
check answer:
(2) +log%28+2%2C+%28x%2B7%29+%29+=+2+%2B+log%28+2%2C+%28x%2B4%29+%29+
(2) +log%28+2%2C+%28-3%2B7%29+%29+=+2+%2B+log%28+2%2C+%28-3%2B4%29+%29+
(2) +log%28+2%2C+4+%29+=+2+%2B+log%28+2%2C+1+%29+
(2) +2+=+2+%2B+0+
OK