25,31 (b) What diameter is required to view a star of magnitude(a) What is the limiting magnitude of a 3.5-inch telesop356 CHAPTER 5 Exponential and Logarithmic Functions14. f(x) = x +2r + 313. f(x) = Vr - 250. Salvageto dep11. f(x) =Sx- 212. (x) =G)the for(d)(a) f(4)(b) g(9)(c) f(-2)16. Change 5 = z to an equjvalent statement involving a logaritnim.whereIn Problems 18 and 19, find the domain of each logarithmic junchon.18. f(x) = log (3x – 2)value(a) F19. H(x) = log2(x² – 3x + 2)20. log:22. 2lo820.4(b)21. In eV2ncolems 23-20, write each expression as the sum and/or difference of logarithms. Express powers as factors23. log324. log2 (a? Vb)* a 0, b 051. Funu 0, v 0, w 0purbe25. log (x Vx + 1) x 02x + 326. In2- 3x + 2)x 2inteboofIn Problems 27-29, write each expression as a single logarithm.un27. 3 log4 x² +2 log, Va52. Fupu28.+희in( + 1)-4m-글[In(x - 4) + Inx]CC29.se30. Use the Change-of-Base Formula and a calculator to evaluate log, 19. Round your answer to three decimal places31. Graph y = log3 x using a graphing utility and the Change-of-Base Formula.53. EIn Problems 32–35, for each function f:(a) Find the domain of f.(d) Find f1, the inverse function of f.(c) From the graph, determine the range and any asymptotes of f(b) Graph f.(e) Find the domain and the range of f.(f) Graph f~1.54.32. f(x) = 2*-333. f(x) = 1 + 3-*34. f(x) = 3e*-2In Problems 36-46, solve each equation. Express irrational solutions in exact form.35. f(x) =n(x+3)36. 86+3x = 437. 3r+x = V341. log, Vx - 2 = 255.40. 252r = 5r-1238. log, 64 = - 339. 5* = 3*+244. log, (x + 3) + log6 (x + 4) = 142. 8 = 4.2545. el-x = 543. 2* .5 = 10"46. 9* + 4.3 -- 3 = 047. Suppose that f(x) = log2(x – 2) + 1.56(a) Graph f.(b) What is f(6)? What point is on the graph of f?(c) Solve f(x) = 4. What point is on the graph of f?(d) Based on the graph drawn in part (a), solve f(x) 0.(e) Find f- (x). Graph f on the same Cartesian planeas f.49. Limiting Magritie of a Telescope A telescope is limit.in its usefulness b the brightness of the star that it is aimat and by the diameter of its lens. One measure of a strbrightness is its magnitude; the dimmer the star, the lagits magnitude. A formula for the limiting magnitude Laltelescope-that is, the magnitude of the dimmest star lican be used to view-is given by48. Amplifying Sound An amplifier's power output P (in watts)is related to its decibel voltage gain d by the formulaL = 9 + 5.1 log dwhere d is the diameter (in inches) of the lens.P = 25e0.1d(a) Find the power output for a decibel voltage gainof 4 decibels.(b) For a power output of 50 watts, what is the decibelvoltage gain?

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Description: 25,31 (b) What diameter is required to view a star of magnitude(a) What is the limiting magnitude of a 3.5-inch telesop356 CHAPTER 5 Exponential and Logarithmic Functions14. f(x) = x +2r + 313. f(x) = Vr - 250. Salvageto dep11. f(x) =Sx- 212. (x) =G)

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25,31 (b) What diameter is required to view a star of magnitude(a) What is the limiting magnitude of a 3.5-inch telesop356 CHAPTER 5 Exponential and Logarithmic Functions14. f(x) = x +2r + 313. f(x) = Vr - 250. Salvageto dep11. f(x) =Sx- 212. (x) =G)the for(d)(a) f(4)(b) g(9)(c) f(-2)16. Change 5 = z to an equjvalent statement involving a logaritnim.whereIn Problems 18 and 19, find the domain of each logarithmic junchon.18. f(x) = log (3x – 2)value(a) F19. H(x) = log2(x² – 3x + 2)20. log:22. 2lo820.4(b)21. In eV2ncolems 23-20, write each expression as the sum and/or difference of logarithms. Express powers as factors23. log324. log2 (a? Vb)* a> 0, b > 051. Funu > 0, v > 0, w > 0purbe25. log (x Vx + 1) x > 02x + 326. In2- 3x + 2)x > 2inteboofIn Problems 27-29, write each expression as a single logarithm.un27. 3 log4 x² +2 log, Va52. Fupu28.+희in( + 1)-4m-글[In(x - 4) + Inx]CC29.se30. Use the Change-of-Base Formula and a calculator to evaluate log, 19. Round your answer to three decimal places31. Graph y = log3 x using a graphing utility and the Change-of-Base Formula.53. EIn Problems 32–35, for each function f:(a) Find the domain of f.(d) Find f1, the inverse function of f.(c) From the graph, determine the range and any asymptotes of f(b) Graph f.(e) Find the domain and the range of f.(f) Graph f~1.54.32. f(x) = 2*-333. f(x) = 1 + 3-*34. f(x) = 3e*-2In Problems 36-46, solve each equation. Express irrational solutions in exact form.35. f(x) =n(x+3)36. 86+3x = 437. 3r+x = V341. log, Vx - 2 = 255.40. 252r = 5r-1238. log, 64 = - 339. 5* = 3*+244. log, (x + 3) + log6 (x + 4) = 142. 8 = 4.2545. el-x = 543. 2* .5 = 10&#34;46. 9* + 4.3 -- 3 = 047. Suppose that f(x) = log2(x – 2) + 1.56(a) Graph f.(b) What is f(6)? What point is on the graph of f?(c) Solve f(x) = 4. What point is on the graph of f?(d) Based on the graph drawn in part (a), solve f(x) > 0.(e) Find f- (x). Graph f on the same Cartesian planeas f.49. Limiting Magritie of a Telescope A telescope is limit.in its usefulness b the brightness of the star that it is aimat and by the diameter of its lens. One measure of a strbrightness is its magnitude; the dimmer the star, the lagits magnitude. A formula for the limiting magnitude Laltelescope-that is, the magnitude of the dimmest star lican be used to view-is given by48. Amplifying Sound An amplifier's power output P (in watts)is related to its decibel voltage gain d by the formulaL = 9 + 5.1 log dwhere d is the diameter (in inches) of the lens.P = 25e0.1d(a) Find the power output for a decibel voltage gainof 4 decibels.(b) For a power output of 50 watts, what is the decibelvoltage gain?

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