1. Prove that (i) Log i = 2 (ii) Log(-5) = ln 5 + ti %3D i) = 3 In 2 + 2 (iv) Log(1+i) = In 2 + 3ri Ti %3D

Q: (a) log,(5x – 1) + 6 = 9 (b) 163x+1 = (4)*-1 %3D (c) In(x + 6) = In(11) – In(x – 4)

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Q: 18. Solve the following logarithmic equation: In(x + 31) – In(4 – 3x) = 5 ln 2. O x = 2 O x = 1 O x…

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Q: 1 1 7. Show that log3 x show your full solution with restrictions log5 x log15 x

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Q: 11. a) Show that e Hence or otherwise evaluate dx leaving your answer in e+1 e*+1 +1 terms of e and…

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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: Question 7 Evaluate: A B с dx (x+1) log(x+1) In 10 In [log(x+1)] + C 1 -In[log(x+1)] +C In 10 -log²…

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Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

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Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

Q: 2. Given that x> 0, the value of x for which log, x + log,(6x + 1'0) = 1 is D

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Q: (1) solve the following  i) 2x/2-16  = 1/32  ii)  log8 (x-2) log8 (x )= 1

A: We have to solve and finding the value of x  Here using logarithmic properties

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 the following: (a) 42x-1 = 64 (d) In 3 – In x – In(x + 5) = 0 (b) 81–x = 4x+2 (c) 22x + 2×…

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Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

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

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Q: 1.  Solve: 32x−1 − 4 · 3x + 9 = 0.

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 5. y = - 5 log , (11x - 4) 6. y = 2 log e 4x°3 7. y = 12x² log 8x 8. y = In 25x 5x3

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Q: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

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: dx Evaluate log - 1+ax 1-ах

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Q: 11 2 log a dx aV6 log r- loga

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

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Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

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Q: 4. Solve the following logarithmic equations. a. 2logx = log2 + log(3x – 4) d. logx + log(x – 1) =…

A: The logarithmic properties; 1). logbmp=plogbm 2). logbm·n=logbm+logbn 3). logbmn=logbm-logbn 4). If…

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 =…

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Q: 5. ƒ(x) = 10* . ex 2x-x2 a. 2 b. logze e 10 c. e*10* + loge e*(x-3) d. x²-4x+4 e. 4x²(3 log, x +…

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Q: given that ln 2 = x, ln 3 = y, and ln 5 = z, express each of the given logarithmic values in terms…

A: Given:   ln 2=x , ln 3=y, ln 5=z   To find:   The logarithmic values in ln 30 in terms of x, y, z…

Q: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

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Q: Determine whether the following statements are true and give an explanation or counterexample.

A: Given information:

Q: QUESTION 15 Solve for x: Log2(3-x)+log2(1-x)=3 T TTF Paragraph V Arial 3 (12p XD Q fx Mashups EE 目

A: Using logarithmic property

Q: d.) In (z+9)– In z = 1 2 log Vx? + 21x = 3 e.) In(x+1) c.) In (x –1) = 2

A: (d) To Find: The value of x. Given: The equation is ln x+9-ln x=1. Formula used: ln a-ln b=ln ab If…

Q: 4 log x + 20 log y- 12 log z

A: We will use basic log properties to solve this

Q: 1/2 (log.(e))" (b) dt. 2t

A:

Q: 4. Solve the following logarithmic equations: a) logx+log(x+15) =2 b) log,(x+1)= 1 +log, x d)…

A: We have to find value of x for given problem

Q: 8.) Evaluate the following natural logarithm problems: a.) ln(1) = b.) ln(2.71828) = c.) ln(4.375 x…

A: .) ln(1) =b.) ln(2.71828) =c.) ln(4.375 x 10

Q: 2 In 2 log2 x dx 7- S

A: Here I am attaching image so that you understand each and every step.

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: 4. Solve the following logarithmic equation: log; (Z + 8)x7 – log3 (2K + 9)x3 = log3 (Z + 5)x2 + 4(Z…

A: Here, Z=9k=5

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: Find the greatest integer less than or equal to log29 S² log2 (x³ + 1) dx + (2x - 1)³ dx.

A: At first, we have to evaluate: I=∫12log2x3+1dx + ∫1log29(2x-1)13dx

Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: rewrite each expression as a singlelogarithm.

A: 35). Given expression is 3log2x+log2y To rewrite the expression as a single logarithm. Solution:…

Q: 1. Express the following as a single log 3log xy-log x +log y a) 6log x b) 3log x c) 6log y d) 3log…

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Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: 3. Solve the natural logarithmic equation. 3 In In x + In In 2 = 4

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.