Log 4 (3x+5) – Log 4 (x+1) = 1
Easy explaination is Log base 4 open parentheses 3x+5 close parentheses minus Log base 4 open parentheses x+1 close parentheses equals 1
2007-11-26 05:03:27 · 4 answers · asked by referencearea 2 in Science & Mathematics ➔ Mathematics
Let log be log base 4 in the following:-
log (3x + 5) - log (x + 1) = 1
log [ (3x + 5) / (x + 1) ] = 1
(3x + 5) / (x + 1) = 4^1
3x + 5 = 4x + 4
1 = x
2007-11-26 07:08:38 · answer #1 · answered by Como 7 · 1⤊ 1⤋
Log 4 (3x+5) - Log 4 (x+1) = 1
The negative sign between the 2 log components means we can rewrite as follows:
Log 4(3x+5) /(x+1) =1
We can also write 1 as Log of 4 to base 4 i.e 1 = Log4 (4)
The original equation then becomes
Log 4 (3x+5) / (x+1) = Log 4 (4)
Since both side of the equation have logarithm to the same base of 4 then they must be equal as follows:
(3x+5) / (x+1) = 4
If we multiply both sides of the equation by (x+1), we arrive at
3x+5 = 4(x+1)
3x +5 = 4x +4
5-4 = 4x -3x
1 = x
x = 1
2007-11-26 05:25:06 · answer #2 · answered by Bisi 2 · 0⤊ 1⤋
x>-5/3 and x>-1 so x>-1
= log 4 (3x+5)/(x+1) =1
If the log is 1 the number is the base bof this log system so
(3x+5)/x+1) = 4
3x+5 =4x+4 and x= 1
2007-11-26 05:13:03 · answer #3 · answered by santmann2002 7 · 1⤊ 0⤋
From properties of logs, this can be rewritten as a single fraction i.e. Log4((3x+5)/(x+1))=1
Therefore,
(3x+5)/(x+1) = 4^1
3x+5 = 4x+4
x-1=0 -> x=1
Therefore x is 1.
2007-11-26 05:09:53 · answer #4 · answered by Fred Gauss 2 · 1⤊ 1⤋