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log2(x+1)−log2(3x−1)=2 · The sum of all the roots of the equation log2(x−1)+log2(x+2)−log2(3x−1)=log24 · The value of x satisfying the following relation: log1/ ... X=1. 刂. * let x=e. A. 12. N. =10.405. X. Page 4. 4) log(x+1)= log(3x-2) = log(2/2). Xug (x+2) = Day (32) | x(x+1)= 2(3x-2). 3x-2. X++. 2. 3x-2 x²+x=6x-4. 2. =0. 12) 6log6 (3x-1). 3X-1. Expand each logarithm. 13) log63x log63+1096X. 14 ... 27) log2(x-4)+5 log2(x+1) - log2(x-1). 26) logsx-4(logsy + 2 logsz) log5x ... 1 x=-2. 14. logg. 15. logs √5 X=1/2. 16. logg 3 X = ½. 17. log2 16 X=4. 18. log1/2 16 X=-4. 27 X=-3/2. Solve for x. 19. log6 x = 2. 20. log5 x = 3. 21. log16 x ... x1, x = 81. 3. Set up equation. 0 = log2(3x – 4) + 1,. -1 = log2(3x – 4). Use log2a = b→ a = 2b. 2-1 = 3x – 4, ½ = 3x – 4. Solve x = 3/2. 4. Use laws of logs. x ≤ 3x + 7 ≤ 4x for all x > 7. b. [2pt] 2x2 + x − 7, x2 x2 < 2x2 + x − 7 ... [2pt] log10 x, log2 x. Follows from log10 x = C log2 x where C = 1/log2 10. The natural logarithm ln(x) is an antiderivative of 1/x, given by ln x ... 1 ≤ x ≤ 2, 2x ≤ y ≤ 3x}. 14. Find the average of the function f(x)=2x ... 1. 3. ) c) log5(81). 21. (8 pts.) Solve: log2(x2 − 3x − 6) − log2(x) = 1. 22. (8 pts.) Arrange the following numbers in order from smallest to largest ... f(x), for rational functions, we divide both the numerator and denominator by the term in the denominator with the highest power of x. Then sim-. log₁ (x)+ 1 = y. Page 2. Honors Math III. Use properties of logarithms to solve for x. 1. logg (3x-1) = logg(x + 4). 3x-1=x+4.