SOLUTION: log2 7x + log2 x = 3

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Question 469442: log2 7x + log2 x = 3
Found 2 solutions by ccs2011, Tatiana_Stebko:
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
use log property
log+x+%2B+log+y+=+log+xy
So
log+7x+%2B+log+x+=+log+7x%5E2
Equation becomes
log+7x%5E2+=+3
Rewrite in exponential form
base of log becomes base of right side with 3 as exponent
7x%5E2+=+2%5E3
7x%5E2+=+8
Divide by 7 on both sides
x%5E2+=+8%2F7
Take square root of both sides

Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C+7x%29+%2B+log%282%2C+x%29+=+3, x%3E0
Use formula log%28c%2Ca%29%2Blog%28c%2Cb%29=log%28c%2C%28a%2Ab%29%29
log%282%2C+%287x%2Ax%29%29+=+3
log%282%2C+%287x%5E2%29%29+=+3
Use formula log%28c%2Ca%29=b<=>a=c%5Eb
7x%5E2=2%5E3
7x%5E2=8
x%5E2=8%2F7
x=sqrt%288%2F7%29=1.069
x=-sqrt%288%2F7%29%3C0extraneous root
Answer x=sqrt%288%2F7%29=1.069