109,115 please Fd the value of log: 3- log, 4. log. (n+ 1) log2. 10e. Find the value of log; 2- log 4-log; 8 log 2.t Find the value of log; 3- log, 4- log, 5- logs 6. log, 7- log, 8. 98. Find the value of log; 4-log,6-log, 8.Ierence Quotient If f(x) - log, x, show that A)-f)- log.1+).Gompressing or stretching, and reflecting. State the domain- express y as a function of x. The constant C is a positive numberSECTION SS Properties of Logarithms 317in+ In CSA. Iny-In(x + C)90. In y-2 in I- In(x+ 1) + In C92. In y- -2x + In C94. In (y + 4) -Sx + In C96. 2 In y- Inx in(+ 1) + In Ctar+ In C- 3)- -4r + lnCa(2x + 1) - In (x + 4) + In CIn ain( + 1) + In Cihat log. (x + V - 1) + log,(x - V - 1) - 0that log. (Va+ Vx - 1) + log.(Vĩ - VI-1) -0that In (1 + )- 2r + In (1 +).f(x+ h) - f(x)log+]) - log, K, show that -/(x) - log x.106. If f(x) - log, x, show that f(AB) (A) + S(B).) - log, K, show that ) - -f(x).Sow that log.N)- log, M - log, N, where a, M, and N.108. If f(x) = log, x, show that f(x) = af(x).110. Show that log,) - -log, N, where a and N are positivepositive real numbers and a 1.real numbers and a+ 1.log, a where aand b are positive real numbers, a 1, and b 1.IL Challenge Problem Show that log, b-112. Challenge Problem Show that log vm- log, m",where a and m are positive real numbers and a 1.A Challenge Problem Show that log, b" = " log, b.shere a, b, m, and n are positive real numbers, a 1,and b1.114. Challenge Problem Find n:log; 3- log, 4- log, 5.... •log. (n + 1) = 10Explaining Concepts: Discussion and Writing5 Graph Y = log (x) and Y; - 2 log (x) using a graphingutility. Are they equivalent? What might sonount for anydierences in the two functions?IK Write an example that illustrates why (log. rlog, x.117. Write an example that illustrates why24log:(x + y) log, x + log: y118. Does 3(-5)- -5? Why or why not?Retain Your Knowledgema 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh inmind so that you are better prepared for the final exam.2V3 - Sx - 4.Ule a graphing utility to solve r- 3 - 4x + 8-0.Round answers to twodecimal placesNilhout solving, determine the character of the solution ofadratic equation 4x - 28r + 49 = 0 in the complex123. Find the domain of f(x) -124. Solve: 4|x + 1 -9

Question

109,115 please Fd the value of log: 3- log, 4. log. (n+ 1) log2. 10e. Find the value of log; 2- log 4-log; 8 log 2.t Find the value of log; 3- log, 4- log, 5- logs 6. log, 7- log, 8. 98. Find the value of log; 4-log,6-log, 8.Ierence Quotient If f(x) - log, x, show that A)-f)- log.1+).Gompressing or stretching, and reflecting. State the domain- express y as a function of x. The constant C is a positive numberSECTION SS Properties of Logarithms 317in+ In CSA. Iny-In(x + C)90. In y-2 in I- In(x+ 1) + In C92. In y- -2x + In C94. In (y + 4) -Sx + In C96. 2 In y- Inx in(+ 1) + In Ctar+ In C- 3)- -4r + lnCa(2x + 1) - In (x + 4) + In CIn ain( + 1) + In Cihat log. (x + V - 1) + log,(x - V - 1) - 0that log. (Va+ Vx - 1) + log.(Vĩ - VI-1) -0that In (1 + )- 2r + In (1 +).f(x+ h) - f(x)log+]) - log, K, show that -/(x) - log x.106. If f(x) - log, x, show that f(AB) (A) + S(B).) - log, K, show that ) - -f(x).Sow that log.N)- log, M - log, N, where a, M, and N.108. If f(x) = log, x, show that f(x) = af(x).110. Show that log,) - -log, N, where a and N are positivepositive real numbers and a 1.real numbers and a+ 1.log, a where aand b are positive real numbers, a 1, and b 1.IL Challenge Problem Show that log, b-112. Challenge Problem Show that log vm- log, m&#34;,where a and m are positive real numbers and a 1.A Challenge Problem Show that log, b&#34; = &#34; log, b.shere a, b, m, and n are positive real numbers, a 1,and b1.114. Challenge Problem Find n:log; 3- log, 4- log, 5.... •log. (n + 1) = 10Explaining Concepts: Discussion and Writing5 Graph Y = log (x) and Y; - 2 log (x) using a graphingutility. Are they equivalent? What might sonount for anydierences in the two functions?IK Write an example that illustrates why (log. rlog, x.117. Write an example that illustrates why24log:(x + y) log, x + log: y118. Does 3(-5)- -5? Why or why not?Retain Your Knowledgema 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh inmind so that you are better prepared for the final exam.2V3 - Sx - 4.Ule a graphing utility to solve r- 3 - 4x + 8-0.Round answers to twodecimal placesNilhout solving, determine the character of the solution ofadratic equation 4x - 28r + 49 = 0 in the complex123. Find the domain of f(x) -124. Solve: 4|x + 1 -9 < 23125. Find the vertex of f(x) = - +4x + 5, and determineumber system.if the graph is concave up or concave down.L Find the real zeros of126. Find the center and radius of the circle- 10x + y + 4y = 35(x) = 5x + 44x + 116 + 95x- 4x - 4-r from -1 to 3.S - 3xeven, odd, or neither?anding or stretching, and reflecting. State the domain A128. Is the function f(x) =the range of f.Vi

Accepted Answer

logaMN = logaM - logaNAssume that x= logaM and y =logaNx= logaM→ M = ax y =logaN→N = ayMN = axay =…

M. log, M Swthat log psitive real numbers and aL log, N, where a, M, and N - 1.