Use the Laws of logarithms to rewrite the expression x14y14 log z19 in a form with no logarithm of a product, quotient or power. After rewriting we have ´x14y14 log = Alog(x) + Blog(y) + C log(z) z19 with A В - and C =

Q: 11. Express as a single logarithm and simplify if possible. log (x2 – 5x – 14) – log (x² – 4)

A: Given query is to simplify the logarithmic expression.

Q: Express In(1+r²) +In r- In sin r as a singel logarithm.

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

Q: How do I expand this log expression? xz/5y x times the square root z over 5y

A: We have to expand the log expression:

Q: log10(2x- 4) = 1+ log10 4, then 'x' is equal to ...............

A: We have to find x

Q: Express x in term of y if: log,xy =2 +2log,x -3log,y

A: Given that:  log4xy=2+2log4x-3log4y We have to express x in the form of y.

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: Without using a calculator, find the exact value of log, 81 – log, 1 log,v 8 – log 0.001

A: To find the exact value of log381-logπ1log228-log0.001. Solution: Properties of logarithm are: 1.…

Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

A:

Q: Express in terms of sums and differences of logarithms. 8 In 3xy 8 In 3 3x°y

A:

Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: Express log (x²/y°) + 4 log y - 6 log Vxy logarithm. as one

A: Given expression is,  logx2y3+4logy-6logxy. It is simplified as follows: logx2y3+4logy-6logxy Apply…

Q: Let a = ln2 and b = ln3. Use the log properties to express the value ln72 in terms of a and b.

A: By using logarithmic property, we express the given logarithm.

Q: Express -log x+5log y as a single logarithm. (A) log -+5y ® log(Vry³) log(V+ y*) (D) log 2

A:

Q: Q5: Evaluate : 1- Domain of: 4-x2 + log10 (x – x)

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the value of y:  logy32=5

A: Given, expression

Q: If log3 (5) = 3y, log; m² = 6 and 2 log; (4) = 4x then what expression (in terms of x and y) is log3…

A:

Q: Use rules of logs to write the log as a single quantity 2log3x - log34     ln x + ln(x+1)

A: GIvenA)2log3x-log34 B) ln x+ ln (x+1)we have to use rules of log to write log as single quantity

Q: 2. Write as a single logarithm with coefficient 1. Simplify as much as possible. Assume the…

A:

Q: Write as a single logarithm. Express coefficients as powers inside the logarithm. 6 In(x) + 3 ln(y)…

A: Here we need to write the given expression  6ln(x)+3ln(y)-7ln(z)-5ln(w) as single expression.

Q: .Express in index notation: a) loga 8 = c ii. Simplify: 3log3 - log 27

A: I.Express in index notation:  a) loga 8 = cAnswerlogam=n ⇒ m=anThereforeloga8 = c ⇒8=ac

Q: 3. Express as a single logarithm: 3 log 2 + log x - log (4x) log(8x) A. log(4x) В. log (2) C. log…

A:

Q: If log base b (x)=0.35 and log base b (z)=0.85. Evaluate the expression of log base b (square root…

A: We have given and we need to evaluate :

Q: 4. (a) Use logarithm properties to expand In ( (@+5)(x – 6)² (x+ 3)3). (b) Rewrite log3(x) + log3 (y…

A:

Q: If logx = 4 and logy =7, then the value of -log is %3D xy

A: Given, logx = 4  and  logy = 7 We have to find the value of  -log1xy.

Q: 11. Write as a single logarithm: 1 log2 X +3 log2 Y - 3 ·log2 Z

A: To write: The expression 13log2X+3log2Y-52log2Z in single logarithm. Formula used: Logarithmic rule:…

Q: Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

A:

Q: 2. Simplify by writing as a single logarithm: Show all steps clearly including use of 'log' rules.…

A: We have to Answer only Question (2) as stated. We know that,

Q: Write the expression as a logarithm of a single ex 1 4 In x- In y 4 Iny-D] 4 In x- %3D 4

A: Using power rule and quotient rule of logarithm,

Q: 1. Find x if log,8x

A:

Q: Expand the log by using the properties of log.

A: The given log function is,

Q: 2log, x-log, y+log, z

A: Follow the procedure given below.

Q: Use the Laws of logarithms to rewrite the expression 3 (212. √/y13 in a form with no logarithm of a…

A:

Q: 10. Express as a single logarithm. 6 log x + log 10 - log(x + 2)

A:

Q: 2. Rewrite as a single log (condense): 7 5, loga (xy®) +12lo9 x12 - 5log. (y) 16,,8 8

A: Answer and explanation is given below

Q: 4) Use the Laws of Logarithms to expand the expression as much as possible. Vx +5 In (2x²/y/

A:

Q: Find the largest value of x that satisfies: log; (x²) – log3(x + 3) = 8 Z Calculator

A: Explanation of the answer is as follows

Q: If (5)** = 16 and log x-y8 =- 3, calculate the values of x and y. %3D

A: lna(b)=y then b=ay  (am)n=amn

Q: 2 log(x+y) = 3log3 +logx + logy

A:

Q: Use the properties of logarithms to expand the expression y8 In x13 z16 in a form with no logarithm…

A:

Q: 2. Rewrite in terms of a single log (condense): (15log. (x) + 10log. (v)]– 7[3lo9. (x) + loga (v)] 5

A:

Q: Write the expression 4lnx-In(y+3) as a single logarithm. 2 Select one: Vy+3 In - In /y+3 4x Зу+6

A:

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: Express as a single logarithm. (a) 4 In(x – 6) – In(x² – 10x + 24) + 2 In(x – 4)

A: The given logarithmic expression is: 4 lnx-6-lnx2-10x+24+2 ln x-4  Since the  logarithmic property…

Q: Write as the natural log of a single expression:(a) 2 ln 5 + 3 ln 4 (b) 5 ln(x1/2) + ln(9x)

A:

Q: Show that 2 + 11n² log,(n³) – 7 = 0(n³)

A:

Q: Express in terms of logarithms of x, y, z, or w.

A: Given: log4z3

Q: 5. Determine an expression in terms of x, y and whole numbers for log, 400 if log 980A

A: Introduction: We will use some logarithmic properties to solve this problem. log(mn)=log(m)+log(n)…

Q: Simplify: (4x*y'z')(16x'y^z*) (18x'y=z}° -2. log , (16 x /8)+ log , (5 x 625) log3x (81x4)

A: We will solve the problem.

Q: solve, g(x)=-3(1/5)x + 2 where g(x)= 0(using log may be) leave it in exact form not decimal.

A: Given that g(x)=0 So we will plug g(x)=0 and solve for x