SOLUTION: Solve: 3^x+1=100. Logarithm Problem.

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Question 701772: Solve: 3^x+1=100. Logarithm Problem.
Found 3 solutions by Edwin McCravy, unlockmath, AnlytcPhil:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
3x+1 = 100

log10(3x+1) = log10(100)

(x+1)10log(3) = log10(100)

%28++%28x%2B1%29log%2810%2C%283%29%29%29%2Flog%2810%2C%283%29%29 = log%2810%2C%28100%29%29%2Flog%2810%2C%283%29%29

%28++%28x%2B1%29cross%28log%2810%2C%283%29%29%29%29%2Fcross%28log%2810%2C%283%29%29%29 = log%2810%2C%28100%29%29%2Flog%2810%2C%283%29%29

x+1 = 2%2F0.4771212547

x+1 = 4.191806549

  x = 3.191806549

Edwin

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let's rewrite this 3^x+1=100 as:
3^x=99
Log (base 3) 99 = x
x=4.1827 (approx)
Make sense?
RJ
www.math-unlock.com

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The above tutor thought you meant

3x + 1 = 100

because you didn't put the exponent in parentheses, which
you should have done.  However I and the first tutor above
knew that by the time you get to logarithms, no teacher would
bother giving you a problem that would waste time to test you
on such a simple basic thing like whether you can subtract 1  
from both sides.  That's too elementary a thing to be testing 
someone already studying logarithms. So I assumed you meant

3x+1 = 100

You can also do it using natural logs instead of logs base 10

3x+1 = 100

ln(3x+1) = ln(100)

(x+1)ln(3) = ln(100)

%28++%28x%2B1%29ln%283%29++%29%2Fln%283%29 = ln%28100%29%2Fln%283%29

++%28x%2B1%29cross%28ln%283%29%29%2Fcross%28ln%283%29%29 = ln%28100%29%2Fln%283%29

x+1 = 4.605170186%2F1.098612289

x+1 = 4.19180655

  x = 3.19180655

Edwin