(a) log, x = log, 27+ 3log, 2 – log, 3 +log, 64 – log, 4 3 without calculator. (b) Prove that: log (p² - q²) – log p (p + q) = log b (P – )| (c) If 33t-2 = 81 and 22s+4 = 47 then find t and st.

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: Solve for x.

A: Given : The equation is , a) log3 x + log3 (x - 2 ) = 1  b) log10 ( x + 3 ) - log10 x = 1

Q: If log(1 +16)+ log(z – 16) =1 then |3| The value of z is

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Q: Log 2 = 0.301,   log 3 = 0.477 and  log 5 = 0.699 Using this information Find:-          a) Log 2/15…

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Q: 1. Given y = log, 256. The value of y= 4 ÷ 2. If log(x + 8) = 3, then the value of x is 1 3. If log,…

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Q: a 0 =c, the z is equal to log c- log a log b 0 log c log b log a log c + log a log b log c log a +…

A: Topic:- algebra

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: 4. If p = a + b + c a. Determine the range of g(x) = e b. If aa = bb = c . -12x-11 ab log.(ab) _ bc…

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Q: Solve the equation.

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

Q: 12. Find r, where log2(ar) – log,(3 – r) = log,(r), and 0 < a < 3. %3D

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Q: 1. The expression log (at) is equivalent to: h logm a log t 1. A. B. log (at)" . log log Wat D. log…

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Q: 23. Solve for x: a) log, (x- 5) + log,(x - 2) = 2 b) 5*+2 - --2500

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Q: 1. Ifļx+1|1 C. -3 2 2. Given that x>0, then value of x for which log, x+log,(6x+10) =1 is А. 5 3. If…

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Q: Given the exponential function f (x) and the logarithmic function g(x), which of the following…

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Q: f the exponential generating function is (ex-1)3, find a formula for a

A: To find the sequence an for the below exponential generating function. fx=ex−13

Q: The solution of the equation Log(z² – 1) = in is| 1,–1. О V2i, – V2i. V2, - V2. O None of them O…

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Q: Determine the principal value of log; 2i A. 1- 0.44li С. 1 — 3.02i B. 0.198- 0.134i D. 1 - 1.73i

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Q: - Tuncuon j(x) = xlog x , then f'(1) is a) 1 b) logx c) x d) None of these O d O a O c O b If f(x) =…

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Q: 1. Given y = log3 9. The value of y= %3D 2. If log(r + 2) = 4, then the value of r is %3D 1 3. If…

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Q: log(ry) = log(r) + log(y) = log(r") = log(r x z x I X ...x x) = log(x) + log(x) + -.= n log(1) Give…

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Q: 2. I. If log a = 3, then a 0.001. II. If log r = -5, then r = 10000.

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Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

Q: 8. Let a be a positive real number not equal to 1. Determine the solution of the equation log, (2x +…

A: To determine the solution of the given equation.

Q: 2 5 Express log b 5.8 m°b in terms of sums and differences of logarithms.

A: The given expression is logbp2q5m5b8.

Q: 11) Given that log, 6= m and log, 5 =n, show that log, 10 = mn+m-1 %3D 12) Solve for x in the…

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Q: Log 2 = 0.301, log 3 = 0.477,  log 5 = 0.699 and log 7 = 0.845 Using this information only, find:-…

A: According to the given information, The given log values are:

Q: (b) Suppose log,(5) = c and log,(2) log, (50) in terms of c and d, but not involving logarithms. d.…

A: objective is to find the expression.

Q: 4. Find all the values of z for which each equation holds. (a) Log(z - 1) = -i.

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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. If r= , then logr can be represented by AB 1) log A+ log B- log C 2) 3(logA? + log B - log C) 3)…

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Q: 5. Show that exp(z²) s exp(2|") for all z e C. Show that Log[(-1+i)']#2Log(-1+i). 7. Find all roots…

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Q: 4 -3 2 1- -8 -7 -6 -5 -4 4. 5 1- (-1,=1) 2 (0, –2) -3 |(1, –4) -4 -5 -6 -7 -8 f (x) =| log (x+

A: We can solve this using given information

Q: MY ANSWER in 4Bola(x-9) -34ln(3X=7)] Using laws of loganienms, wnite the expression belaw…

A: Given: Rewriting above expression, we get:

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

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Q: a) If log:3 b) Solve for x if log,o(8x+1) – log10(2x + 1) = log1o(x+2) = a and log105 = b, write…

A: (a) Here given as log103=a, log105=b log1075=log103×52=log103+log1052=log103+2log105=a+2b (b)…

Q: 3 Given that xand y are real numbers, x>0, if 4"-3x' 16, log, x=, r+1 y find the value of x

A: Given: x and y are two real numbers, x&gt;0 4x-3xy=16 log2x=x+1y We can write, 4x=16 +3xy⇒2x2=16…

Q: 4. I. The simplified form of 4 log, " +5 log2 -3 log, z is log2 II. The expanded form of log, p is 2…

A: There are four following math lagarithm formulas

Q: 3. Solve for x: log, (x+6)- log,(x-2) = 2 4. Solve for x: log, (x-5)+log,(x+1) = 4

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Q: x- log, (x – 6) = log , 9 4) log, (x– 10) + log, 4 = 3 %3D g7 g, (x + 3) – log, x = 1 6) log, 8 +…

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Q: (a) Solve the following: -1 (i) 2*-6 8 (ii) log, (x+3) = 1– log, (x-1)

A: An equation is a formula that provides the equality of two expressions, by connecting them with the…

Q: Find the value of log(-2). o 0.3 + 1.364i O -0.3 - 1.364i O 0.3 - 1.364i O -0.3 + 1.364i

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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: 4 Given that log 20.571, log 4≈ 1.141, and log 6≈ 1.476, find log n 4 log nr (Type an integer or a…

A: This question is from logarithm and its property

Q: - 4 ) if f(x)= log3 3-2 (x3 – 4) (x3 – 2)In(3) 6x? %3D (..3 ..3

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Q: if f(x) = loge 4x then f (3) is: 1/3 1/12 2 log, 12 4 loge 4

A: Given:         To determine:

Q: log, 5 z 0.699 and log, 2x 0.301. Use one or both of these values to evaluate loga 125.

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Q: Find the value of the base b so that the graph of f(x) = log,(x) contains the given point. (1/8, 3)…

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Q: T + log, (V27 - 2") sin 24-1 + log, (log; (915) + п1+(-1)17 + 1) + (-1)5 + (-1)27 (-1)766 25 – 24 –…

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