SOLUTION: log10a+log10(a-6)=2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log10a+log10(a-6)=2      Log On


   

Question 940229: log10a+log10(a-6)=2
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log10a+log10(a-6)=2
--------------
log10[a(a-6)] = 2
-----
a(a-6) = 10^2
----
a^2 - 6a - 100 = 0
----
Positive solution:
a = 13.440...
Cheers,
Stan H.
---------------

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Express 2 as a log
+2+=+log%28+100+%29+
+log%28+a+%29+%2B+log%28+a+-+6+%29+=+log%28+100+%29+
+log%28+a%2A%28+a+-+6+%29+%29+=+log%28+100+%29+
+a%2A%28+a+-+6+%29+=+100+
++a%5E2+-+6a+-+100+=+0+
----------------------
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-6+
+c+=+-100+
+x+=+%28+-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2+-+4%2A1%2A%28-100%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+6+%2B-+sqrt%28+36+%2B+400+%29%29+%2F+2+
+x+=+%28+6+%2B-+20.881%29+%2F+2+
+x+=+26.881%2F2+
+x+=+13.441+
------------------
check answer:
++13.441%5E2+-+6%2A13.441+-+100+=+0+
+180.66+-++80.646+-+100+=+0+
+100.014+-+100+=+0+
close enough