1. log, 2x-log, 2 = log(2x-1),

2. log3(4x+8) - log3 2 = log(x+5),

3. In(x² - 2x) - Inx = ln(2x-5),

4. lg(x²-4) 1g(2+x) = 1g(3x-8), -

5. 1g2lg(x + 1) = lg 3 − 1g(x +

2. log3(4x+8) - log3 2 = log(x+5),

3. In(x² - 2x) - Inx = ln(2x-5),

4. lg(x²-4) 1g(2+x) = 1g(3x-8), -

5. 1g2lg(x + 1) = lg 3 − 1g(x + 2),

6. log5(x+4)-logs 2 = log5(x-3)

7. log, 28-log7(x+4)= log, 4,

8. log47 - log4(2x+1)= log4 14,

9. 2log2x-log2 4 = log(2x-4)

Sure, I can help you solve these logarithmic equations.

1. log(2x) - log(2) = log(2x-1)
Simplifying the left side using log rules, we get:
log(2x/2) = log(2x-1)
2x/2 = 2x-1
x = 1

2. log3(4x+8) - log3(2) = log(x+5)
Using log rules again, we simplify the left side:
log3((4x+8)/2) = log(x+5)
log3(2x+4) = log(x+5)
2x+4 = x+5
x = 1

3. ln(x² - 2x) - ln(x) = ln(2x-5)
Using ln rules, we simplify the left side:
ln((x² - 2x)/x) = ln(2x-5)
(x² - 2x)/x = 2x-5
x - 2 = 2x² - 5x
2x² - 6x + 2 = 0
x² - 3x + 1 = 0
Using the quadratic formula, we get:
x = (3 ± sqrt(5))/2

4. lg(x²-4) + lg(2+x) = lg(3x-8)
Using lg rules, we simplify the left side:
lg((x²-4)(2+x)) = lg(3x-8)
(x²-4)(2+x) = 3x-8
2x³ - 5x² - 6x + 32 = 0
Using synthetic division, we get:
(x-2)(2x² - x - 16) = 0
x = 2, (1 ± sqrt(65))/4
But x = 2 doesn't satisfy the original equation, so we discard it.
Therefore, x = (1 ± sqrt(65))/4

5. lg(2lg(x + 1)) = lg 3 - lg(x + 2)
Using lg rules, we simplify the right side:
lg(2lg(x + 1)) = lg(3/(x+2))
2lg(x + 1) = 3/(x+2)
2lg(x + 1) = lg(10) - lg(x+2)
2lg(x + 1) + lg(x+2) = lg(10)
Using lg rules again, we simplify the left side:
lg((x+1)²(x+2)) = lg(10)
(x+1)²(x+2) = 10
x³ + 3x² - 6x - 7 = 0
Using synthetic division, we get:
(x+1)(x² + 2x - 7) = 0
x = -1, (-2 ± sqrt(20))/2
But x = -1 doesn't satisfy the original equation, so we discard it.
Therefore, x = (-2 ± sqrt(20))/2 = -1 ± sqrt(5)

6. log5(x+4) - logs(2) = log5(x-3)
Using log rules, we simplify the left side:
log5((x+4)/2) = log5(x-3)
(x+4)/2 = x-3
x = 11

7. log28 - log7(x+4) = log4(8)
Using log rules, we simplify the left side:
log2(8/(x+4)) = log4(8)
8/(x+4) = 2³
x = 4

8. log47 - log4(2x+1) = log4(14)
Using log rules, we simplify the left side:
log4(7/(2x+1)) = log4(14)
7/(2x+1) = 2²
x = 3/2

9. 2log2x - log24 = log(2x-4)
Using log rules, we simplify the left side:
log2(x²) - log2(4²) = log(2x-4)
log2(x²/16) = log2(2x-4)
x²/16 = 2x-4
x² - 32x + 64 = 0
(x-16)² = 0
x = 16 (multiplicity 2)