In parts (a)–(c), graph f and g in the same viewing rectangle. a. f(x) = ln(3x), g(x) = ln 3 + ln x b. f(x) = log(5x2), g(x) = log 5 + log x2 c. f(x) = ln(2x3), g(x) = ln 2 + ln x3 d. Describe what you observe in parts (a)–(c). Generalize this observation by writing an equivalent expression for logb(MN), where M > 0 and N > 0. e. Complete this statement: The logarithm of a product is equal to  ______________.

Q: The graph of a logarithmic function is given.Match each graph to one of the following function

A: Given, graph where y=0 at x=3 y=log3x-1 satisfy this given graph  put x=3 y=log33-1y=1-1=0 now find…

Q: 18. Find the domain and range of g(x) log2(x+3).

A: Domain of log is always greater than 0 .

Q: Condense each logarithmic expression.

A: We have to condense the following logarithmic expressions -  (a) 12log x + 3 log(x+1)⇒ log(x)12 +…

Q: Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o…

A: Given

Q: Solve each equation.

A: According to logarithimic rule , . If , then .

Q: given log10 x = 2 and log10 y = -1. show that xy-100y2 = 9

A:

Q:

A: By definition, The logarithmic function y=logax is defined to be equivalent to the exponential…

Q: Solve the equation.

A: Given, log3x-2=log327-log3x-4-5log51 solve the equation log3x-2+log3x-4=log333-1…

Q: The graph of g(x) = 5 + log2 x is the graph of f(x) = log2 x shifted _______.

A:

Q: 9. (x) = log(1-2x)

A:

Q: Evaluate: A B С) D (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 1 -In 10 log² (x + 1) + C 2 In 10…

A: Given problem:-

Q: (x-2) log.(x2 - 4) – 2 log (x-2) + loga (x+ 2)

A:

Q: The graph of every exponential function f(x) = ax , where a > 0 and a ≠ 1, passes through three…

A: f(x)=ax

Q: 9. Condense (log4x – log4y)+2 log4(x+1) into a single logarithm with a coefficient of one.

A: Explanation of the answer is as follows

Q: 1) Solve a) log(x+4)=1 b) log, (2x-3)=2

A: Given problems :- log(x+4)=1  log5(2x-3)=2

Q: The graph of g(x) = log3(x + 5) is the graph of f(x) = log3 x shifted_______.

A: Given: The function gx=log3x+5 and the function fx=log3x To compare: The graphs of given function.

Q: If log3(3x +5) – log3(9x) = 2 then enter your answer for x as a fraction in its lowest form

A:

Q: If f(x) = 3 log4 (x+2) - 1 and F(g(x)) = g(f(x)) = x, then what is g (x)?

A:

Q: [ Зх +1 x – 3 A 3x + log (x- 3) 3x + 10log (x- 3) в Зх + log. (x- 3) +с 3x + 10log (x – 3) + c

A:

Q: The graph of g(x) = log;(x + 5) is the graph of f(x) = log3 x shifted

A: gx=log3x+5 and fx=log3x

Q: x² 6 + ,X log (x² + 7)(x³ – 5)² -

A: Laws of Logarithm:

Q: (1) (a) Solve the following: 1 (i) 2*-6 (ii) log;(x+3)=1-log;(x-1)

A:

Q: 3) In x-log x = 1. Answer should be in the natural exponential form. %3D

A: This is complicated and lengthy problem, so I can do it in Advanced Mathematics.

Q: Find the domain, range, x- and y-intercept of  f(x)=log3(x+3)-2 f(x)=ln(2x+2)-1

A:

Q: Sketch on graph a) y = 2x-3+ 3  b) y = log2 (x – 4)

A: a)

Q: Approximate x to three significant figures .

A: x=log 8.4 , b. log x=-2.4260 c. ln x=1.8

Q: Find the domain of the logarithmic function. f(X) = In (x² = x-6)

A:

Q: Give five examples of exponential functions in the form f(x)=bx and f(x)= a*bP(x)+h with its domain…

A: we have to give five examples of exponential functions with its domain and range.

Q: a) In (x – 7) = 6 (b) In (x + 9) + In (x- 9) = 1 (c) log sx - log 52x = 2

A:

Q: 1. In 2x - 21n/2y³ + In(xy)² as a single logarithm.

A: since you have posted multiple question i can do first question as per pur company guidelines please…

Q: Find the exponential function  f(x) = Ca^x whose graph goes through the points (0,2) and (2,8)

A:

Q: The graph of g(x) = -log4x is the graph of f(x) = log4x reflected about the______ .

A: Given that graph of f(x)=log4x and g(x)=-log4x.

Q: 2log x-1=log(x-1)

A: Given:  2logx -1=log(x-1)we know that alogb =logba   then 2logx=logx2Then    logx2-1=log(x-1)…

Q: Solve for x. (a) In (x – 3) = 7 (b) In (x + 4) + In (x - 4) = 1 (c) log gx² - log ,2x = 3

A:

Q: QUESTION 16 Find the domain of f(x)=log(x – 7)-

A:

Q: 25^x-2 = 5^3x   3e^-5x = 132   -4(5^x) = -68   e^2x-7e^x+10=0   ln3x = 8.2   log(x+2) -…

A:

Q: The graph of g(x) = log5(-x) is the graph of f(x) = log5 x reflected about the________ .

A: The graph of gx=log5-x is the graph of fx=log5x reflected about the________.

Q: 2. Solve for x. 45x-x² = 4-6 a. b. (1 − x)5 = (2x − 1)5 - 60 c. 55 = 1+5e-0.6x d. 3 log x + 10 =…

A:

Q: Example 9: Solve the following for the exact value of x a) log,xlog, 27+2 log, 2-log, 3 b) logx+log…

A: Refer to the question we need to find the value of x of the provided logarithm equations as,

Q: 3. 2 log x< log (2x-1)

A:

Q: Given that the point (35,6)is a point on the graph of g(x)=log2(x)what is the corresponding point on…

A:

Q: 3. Give the domain and range of the exponential graph. f(x) (0,2)

A: Domain :- The values on the X axis for which we get the curve of the graph. Range :- The…

Q: 5. If log 0.3 (x-1) < log 0.09 (x-1), then x lies in the interval c. -2 <x<-1 d. 1<x< 2 a. 2<x < b.…

A: If log0.3(x-1)&lt;log0.09(x-1)

Q: Find the exponential function that passes through the points ( – 3, 405) and (1, 5) - f(x) =

A:

Q: Find the equation of an exponential function of the form f(x) = a · bº that passes through the…

A:

Q: 13. 3*-5 -4 14. In(x – 2) = 4 %3D 15. log(x + 9) + ipgx = 1

A:

Q: 1. solve for x, log2(3x-2)=4.    2. use the laws of logarithims to rewrite 7log x - 3log y as a…

A:

Q: If log (x + 7) – log, (7x) = 4 then enter your answer for æ as a fraction in its lowest form

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the value of a so that Screen Shot 2021-10-06 at 8.48.07 AM.png 3ªx2 – 4x + 7 lim log3 = 4 3x2…

A: NOTE: As per our guidelines, I have solved first problem. If you want the answer of other, kindly…

Q: If log1,5 + log10 (5x + 1) = log10 (x+5)+1, then x is equal to :

A: Given data is : log105+log105x+1=log10x+5+1 To find the value of x . Use the property of logarithm :…