# 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

 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) = -2 d) log (7x + 9) - logx = 1 b) log (3x-2) = 1 e) 2logx - log (4x-3) = 0 c) log (2x) + log4 = 3 f) 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 + log3 d) 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

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

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

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

TOPExercise 6
 Six simple exponential equations that can be solved without logarithms: a) 5x = 15'625 b) 22x = 64 c) 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 + 2 c) 7x+8 . 7x-1 = 735 b) 34x-1 . 92x + 1 = 27x. 35x + 1 d) 82x-1 - 43x-1 + 26x-1 = 96
SOLUTION

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

TOPExercise 9
 Six simple exponential equations that require logarithmizing both sides of the equation: a) 23x = 5 b) 53x-2 = 7 c) 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-x d) 4x-1 - 9x = 32x-1 - 22x + 1 b) 5x + 6x = 6x + 1 e) 22. 5x - 22x = 22x + 2 c) 2x + 1 - 3x = 3x-1 - 2x f) 24x + 24x + 5 = 99
SOLUTION