SOLUTION: Hello, I have a question, i've done almost all my homeworks, but there are 2 more, and they are logarithms, with equations and I really don't see how to do them. Could you please

Question 970412: Hello, I have a question, i've done almost all my homeworks, but there are 2 more, and they are logarithms, with equations and I really don't see how to do them.
Could you please help me ?
log3(x+1) - log3(x) = 1

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
log3(x+1) - log3(x) = 1
use logarithm difference rule
log3( (x+1) / x ) = 1
use definition of logarithm
(x+1) / x = 3
multiply both sides of = by x
x+1 = 3x
subtract x from both sides of =
2x = 1
divide both sides of = by 2
x = 1/2 = 0.5
****************************
check answer by substituting for x in original equation
log3(0.5 + 1) - log3(0.5) = 1
log3(1.5) - log3(0.5) = 1
log3(1.5/.5) = 1
log3(3) = 1
1 = 1
answer checks

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