SOLUTION: solve each: (Can you please provide steps. i would really appreciate it. It would help me to better understand.) 1.) log base (x+2) of 16 = 4 2.) log base 3 of x + log bas

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve each: (Can you please provide steps. i would really appreciate it. It would help me to better understand.) 1.) log base (x+2) of 16 = 4 2.) log base 3 of x + log bas      Log On


   

Question 475999: solve each:
(Can you please provide steps. i would really appreciate it. It would help me to better understand.)
1.) log base (x+2) of 16 = 4
2.) log base 3 of x + log base 3 of (x-2) = 1





Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
1.) log%28%28x%2B2%29%2C+16%29=4
Formula log%28c%2Ca%29=b <=> a=c%5Eb
16=%28x%2B2%29%5E4
We can look at 16 like at 2%5E4
2%5E4=%28x%2B2%29%5E4
x%2B2=2
x=2-2
x=0
Check log%28%280%2B2%29%2C+16%29=4
log%282%2C+16%29=4
log%282%2C+2%5E4%29=4
4=4 correct
.
.
2.) log%283%2Cx%29+%2B+log%283%2C%28x-2%29%29+=+1
system%28x%3E0%2Cx-2%3E0%29 => system%28x%3E0%2Cx%3E2%29 => x%3E2
Use formula
x%28x-2%29=3%5E1
x%5E2-2x-3=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+16%29%29%2F2+
x+=+%282+-+4%29%2F2+=-1%3C2 the extraneous root
x+=+%282+%2B4%29%2F2+=3
Answer: 3