Write as a single logarithm
log(x+1)+2log(2x+1)-log(x-3)
log ( a ^ n ) = n * log ( a )
log ( a * b ) = log ( a ) + log ( b )
log ( a / b ) = log ( a ) - log ( b )
log ( x + 1 ) + 2 log( 2 x + 1 )- log( x - 3 )=
log [( x + 1 ) * ( 2 x + 1 ) ^ 2 / ( x - 3 ) ]
I keep getting wrong answer, its not the same as the book :3
To write the expression as a single logarithm, we can use the properties of logarithms:
1. First, we can combine the two logarithms that have addition/subtraction inside. In this case, we have log(x + 1) - log(x - 3):
= log[(x + 1)/(x - 3)]
2. Then, we can combine the two logarithms that have multiplication inside. Here, we have log[(x + 1)/(x - 3)] + log(2x + 1)^2:
= log[((x + 1)/(x - 3)) * (2x + 1)^2]
3. Finally, we can simplify further if needed, but in this case, we cannot simplify any further.
Therefore, the expression log(x+1) + 2log(2x+1) - log(x-3) can be written as a single logarithm: log[((x + 1)/(x - 3)) * (2x + 1)^2].