51-56 - Combining Logarithmic Expressions Combine into a single logarithm. 51. log 6 + 4 log 2 52. log x + log(x³y) + 3 log y 53. log:(x – y) – 2 log:(x² + y²) 54. log, 2 + log,(x + 1) – log,(3x + 7) 55. log(x – 2) + log(x + 2) – log(x + 4) 56. [In(x – 4) + 5 In(x² + 4x)]

Q: O log (x)+Log (x-1) = log (8X-12)-1eogL2) %3D Ans/x= 2,3

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

Q: 1. lim (2*+5 - 7) 6. lim (ln3x -- 8) - 7 X-5 x--3 2. lim (22x-1-3) 7. lim log2 (x² + 4x + 4) w X-3…

A: 1) Given:                  limx→52x+5-7 Plug in the value x = 5                 =25+5-7=210-7=1017…

Q: (x+4)² inx-2) 9 3 Express In in terms of In x, In (x+4) and In (x-2). 5, Select one: 2 1 9 In x -In…

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Q: logarithms to find an exact solution for   ln(5)+ln(5x2−3)=ln(154).   If there is no solution,…

A: Given query is to find the value of x.

Q: 2 Express log b 3. x in terms of logarithms of x, y, and z. Choose the correct expression below. O…

A: Given equation : logbx2y3z

Q: 5. The height of a drone in m over time in minutes is given by f(x) = 3 - log ,(x - 1). The height…

A: Given query is to find the time when height of the drone will be same.

Q: 9. 8) logx -2 4. 3. I|

A: we have to find logx34=-23

Q: ii) 2 log, (x)– log2 (3x – 4) = log, (x – 1) – 1

A: We make the coefficient 2, exponent inside the log.  And for 1 we replace it by log22 because…

Q: 11) The Inverse of ()= *-1* a)(x) 3x-1 b)/(x) log2(x) d)f(x)= log3(Vx+1) e) non

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Q: (5-3x^2)^7 (square root 6x^2+18-12) how would this be solved using logarithmic differentiation?

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Q: 7) log-2(-8) = x 8) logix = 5 2 9) 2* + 2* = : 10)3*+2 = 92x-3 2

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Q: 51–56 ■ Combining Logarithmic Expressions Combine into asingle logarithm

A: (51)        Given: log 6 + 4 log 2 Apply: k.log m=log mk             =log 6 + log 24 Use:  log M+log…

Q: 10- 11- 12- In 2 log₂x X 2 log10 (x + 1) x + 1 dx x log10 x 0 S -dx -dx

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Q: tan -1 (i – 3) = Log O -2 i-11 + i8 + i2kπ Log i-1|+i0+ i2kㅠ Log i-11-18+i2kㅠ | O 2 3 + 18-12kㅠ Log…

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Q: log31 = logo(1- 4x) log(3x- 2) 5 log, y +5 log2 4 log x = r(x) %3D h(x) = logs 3+x

A: Given: We have to identify the given as function, equations, and inequality. The function can be…

Q: Log(-z + 2) = i2 4

A: Consider the given expression, ln14z4+2=i2π The complex number is represented in three ways,…

Q: 2 log, u - 3 log, 4 log, V -

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Q: 4. If log, 2(x + 6) =log, 36, then the value æ is 5. If log, æ = 0.5 and log, y = 1.16, then the…

A: We have to solve given logarithm equations. In the first equation we have to find the value of x.…

Q: Write each expression as a single logarithm

A: Given,

Q: solve the logarithmic equations.

A: As per guidelines, we are supposed to solve only first three questions. Please repost other…

Q: 6. 1- x Find the area of the region bounded by thex-axis, the y-axis, and the graph of y = 2- 2x +…

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Q: 9–16 ■ Exponential Form Express the equation in exponentialform.

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Solve (a) x = log3 1/81 (b) log x 1/16= -2

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Q: #32

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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

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Q: 41. (a) log,(¿) (b) log10 x = –3 = X 42. (a) log, 1000 = 3 (b) log, 25 = 2 43. (a) log, 16 = 4 (b)…

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Q: 2..3 I. 1.The expression log is equivalent to (2logx + 3logy - logz) 2) (2logx + 3 logy) – logz | 3)…

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Q: 1) f(x) = Vx- 3+ V5-x 2) f(x) = /3 – log2 x2- (log2 x)² %3D %3D

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Q: True or False: 1. All exponential functions of the form f(x)=a^x−h +k, where h and k are real…

A: To answer the given questions about exponential and logarithmic function.

Q: 7. log;(x²) =, x log5(_ 8. log,(y*) = x log-(. 9. log(V1000) = – x log( %3D

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Q: 2. In (x + 2) + In 2 = 3 | 4. log:9 – logs (x+ 10) = 1 6. log, (x² +3x) – log, (x + 5) = 1

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Q: Method 2: 51-3 = 10 => log, (5-) = log, 10 t-3 = log, 1C by(2) a) 4·73t-1 = 7 35t b) 7 – 4 = 6 c)…

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Q: 1 =-5 log2 32

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Q: tan -' (i – 3) = Logi-1+ i0 + 12*T -2 Log i-1 -1- i0 + i2kn Log -1+ 10 + i2kT| O 2 2 -i-1|+i8-12kπ 3

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Q: 4-2-2 a -2 andx 0 -2 -3x+4 b. log,2 2x-1 1-1 B+2--+2 d. and 1 e. no solution

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Q: 43. Graph f(x) = 4x and g(x) = log4 x in the same rectangular coordinate system. 44. Graph f(x) =…

A: 43) Graph

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: log(-x + V 2 log -x + x² + 1}• log{x + Vxn ,2 + V x +1

A: use property of logarithm.

Q: I .   Solve for  x:     log 10  ( x   +  6  ) +   log10 ( x  -  6 ) =   2…

A: We have to solve for x: log10(x+6)+log10(x-6)=2and  12loga(x+2)+12loga(x-2)=23loga27

Q: Some biorlogos model thenumberof S species in afixed area A (e.g. an island) with therelationto…

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Q: Please I want solution with all steps. Many thanks

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Q: 5. log7 (4) = 7. log(x²+36) = 2 =log, (x-3)

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

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Q: (1093x-21093x+5) The equation log3x-2 X exactly three real solutions at least one real solutions =…

A: Consider the given equation, xlog32x-92log3x+5=33 Let us assume that log3x=m,…

Q: d) ln 3 − ln x − ln(x + 5) = 0 (e)log4 (x + 2) − log4 (x − 1) = 1 (f) log2 (x − 1) − log2(x - 1) -…

A: We have to solve the following equation for x.

Q: 89+3 12 89+3 12 ) log( ) = log( log( log( ----- L-----

A: To solve the given expression

Q: 9. -2 8) logx 4 3.

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Q: 3) log 5x- log 8 = 3 4) log, x+ log, (r+ 1)= log, 2

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Q: 5. If log, x = 0.3 and log, y = 1.24, then %3D the value of log, x°y = %3D

A: logax3y3=logax3+logay3 logax3y3=3logax+3logay using the given data, we have logax3y3=30.3+31.24