What is Log 6 1

Exponential equations and
logarithmic equations



Simple logarithmic equations: 1, 2, 3

More difficult logarithmic equations: 4, 5

Exponential equations: 6, 7, 8, 9, 10



Overview of the procedures



All tasks on one page for printing






TOPTask 1
Solve the following logarithmic equations by putting them in the form loga = b and then raising them to the power of 10.
a)log (x-5) = -2d)log (7x + 9) - logx = 1
b)log (3x-2) = 1e)2logx - log (4x-3) = 0
c)log (2x) + log4 = 3f)logx + log (x + 2) - log3 = 0
 SOLUTION



TOPexercise 2
Solve the following logarithmic equations by putting them in the form loga = logb and then raising them to the power of 10.
a)logx + log (x-7) = log6 + log3d)log (x-5) - log2 = log (3x)
b)log (x-3) - log6 = log7 - log (x-4)e)2log (x + 1) - logx = log4
c)log (35-x3) = 3log (5-x)f)4logx = 2log (x2-3x)
 SOLUTION



TOPTask 3
Two tasks with a different basis. Try to solve them using the same pattern:
a)log2(x + 14) - log2(2x) = 2b)log2(x + 3) + log2(x-2) = 1 + log2x
 SOLUTION



TOPTask 4
First, solve the quadratic equation:
a)2 (logx)2-5logx-3 = 0b)(log2(x))2 - 7log2(x) + 12 = 0
 SOLUTION



TOPTask 5
The following tasks can be solved if you take both sides logarithmically:
a)x1 + logx = 102b)x3 = 10x1 + logx
 SOLUTION



TOPExercise 6
Six simple exponential equations that can be solved without logarithms:
a)5x = 15'625b)22x = 64c)10x = 100-1.5
d)e)f)
 SOLUTION



TOPExercise 7
Four more difficult exponential equations that can be solved without logarithms:
a)23x-4 . 42x-3 = 8x + 2c)7x+8 . 7x-1 = 735
b)34x-1 . 92x + 1 = 27x. 35x + 1d)82x-1 - 43x-1 + 26x-1 = 96
 SOLUTION



TOPExercise 8
Six problems that lead to quadratic equations:
a)32x - 12 . 3x + 27 = 0d)4x + 1 - 2x + 4 = 128
b)4x - 12 . 2x + 32 = 0e)25x + 1 + 3 . 5x + 2 - 16 = 0
c)22x-1 - 3 . 2x + 4 = 0f)4x + 1 + 16x-1 = 1536
 SOLUTION



TOPExercise 9
Six simple exponential equations that require logarithmizing both sides of the equation:
a)23x = 5b)53x-2 = 7c)2x-2 = 5x-1
d)e)f)3x-1 . 22x = 53x + 1
 SOLUTION



TOPExercise 10
Six more difficult exponential equations that sooner or later have to use logarithms:
a)2x-1 . 52x-1 = 31-xd)4x-1 - 9x = 32x-1 - 22x + 1
b)5x + 6x = 6x + 1e)22. 5x - 22x = 22x + 2
c)2x + 1 - 3x = 3x-1 - 2xf)24x + 24x + 5 = 99
 SOLUTION