2 easy log question

1.
log(4x - 1) = log5(2x + 1) - 1
log(4x - 1) = log5(2x + 1) - log10
log(4x - 1) = log[5(2x + 1)/10]
log(4x - 1) = log[(2x + 1)/2]
4x - 1 = (2x + 1)/2
8x - 2 = 2x + 1
6x = 3
2x = 1
x = 1/2


2.
log4(5x - 3) = log4(3x + 1) - (1/2)
log4(5x - 3) =log4(3x + 1) - (1/2)log4(4)
log4(5x - 3) =log4(3x + 1) - log4(4)^(1/2)
log4(5x - 3) =log4(3x + 1) - log4(2)
log4(5x - 3) =log4[(3x + 1)/2]
5x - 3 = (3x + 1)/2
10x - 6 = 3x + 1
7x = 7
x = 1

2013-03-02 19:45:02 補充：
另法：

1.
log(4x - 1) = log5(2x + 1) - 1
log5(2x + 1) - log(4x - 1) = 1
log[5(2x + 1) / (4x - 1)] = 1
5(2x + 1) / (4x - 1) = 10
(2x + 1) / (4x - 1) = 2
2x + 1 = 8x - 2
6x = 3
x = 1/2 ...... (答案)


2.
log[base4](5x - 3) = log[base4](3x + 1) - (1/2)
log[base4](3x + 1) - log[base4](5x - 3) = 1/2
log[base

2013-03-02 19:45:40 補充：
2.
log[base4](5x - 3) = log[base4](3x + 1) - (1/2)
log[base4](3x + 1) - log[base4](5x - 3) = 1/2
log[base4]{(3x + 1)/(5x - 3)} = 1/2
(3x + 1)/(5x - 3) = 4^(1/2)
(3x + 1)/(5x - 3) = 2
10x - 6 = 3x + 1
7x = 7
x = 1 ...... (答案)

1.
x = 1/2

2.
x = 1