64 J2C48=X Log,

Q: Express using a single log            2Log a2 – Log b – 2 Log a2b + 2Log b

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Q: 2 Find x so that log10 x = log, 10

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Q: Q6.Differentiate w.r.t'x 1-logr

A: we have to derivative

Q: 3 1. y = logVV12x %3D

A: 1. Given function is y=log12x3. Solution: We know that, logab=b loga Given function can be…

Q: 101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

A: To show: loga(x+x2-1)+loga(x-x2-1)=0 Solution: loga(x+x2-1)+loga(x-x2-1)=0 Considering, Left Hand…

Q: Differentiate f (x) = log6 (x26"

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Q: Differentiate the function

A: Before we get into solving the question, let's look at the two derivtives shown on the white…

Q: Show that log, (Vx + Vx – 1) + log.(Vx – Vx – 1) = 0.

A: To show that logax+x-1+logax-x-1=0. Solution: We know that, logm+logn=logmn Simplifying the left…

Q: Express the following using a single log: 3Log ab2 -Log a2b - 4 Log a/b - 3Log b2

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Q: 3. Expand the logarithms below: log,(3x'y^y' b. log log (– 2a²b*)* а.

A: Solution:  The objective is to expand the given logarithmic functions

Q: 4. Differentiate the function. f(x) = log3 (x In x)

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Q: Express the given quantity as a single logarithm. 2)2 In(x 2)7In x - In(x2 +

A: Let the given expression is:

Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

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Q: Prove that | log,x| E O(log2 x )

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: log (x2) - log(v9) + log(z4) condensed into a single logarithm is expressed as log() Select one: O…

A: Expression is given by logx2 - logy + logz4 To evaluate : Single logarithmic expression.

Q: 2 log, (x) = 2

A: The given equation is: 2 log4(x) = 2

Q: Differentiate f(x) = log, (9 – 10x).

A:

Q: Express th equation in exponential form.

A: Logarithm equation can be converted to exponential using the following properties of a logarithm.…

Q: Use the logarithm identities to obtain the missing quantity. 2 log,(p) – 4 log,9) – 3 log,(r) = log,

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Q: Prove that : log 2 xp

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Q: Rearrange this equation to isolate A. H = K + log () A =

A: we have to rearrange the equation to isolate A

Q: Which of the following is equivalent to 142 = X? O logx(14) = Z O log x(Z) = 14 O log14(Z) = X O…

A: The objective is to find the correct option.

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√2

A: Solution:- the given term is A=ln(32) as we know that  ln(m×n)=lnm+lnnand ln(a)b=bln(a)

Q: (b) 2log(x – 3) – log(x – 1) = 0

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Q: Differentiate: V=log, (x'+x)

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Q: 5) Show the proof that loga M" = r· loga M

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Q: Express as a single logarithm with a coefficient of 1: 1/2 logb x - logb(x2 + 1).

A: logmt-logms=logmtsa logmn=logmna

Q: Differentiate f (x) = loge (x26")

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Q: 4. S(x) = log,(-x)

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Q: (b) 8[log(2-j3)]e

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Q: Determine the approximate values af log3 (VI6,0L + V24.99 (Instruction d logax dx In a

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Q: (ii) Form the PDE by elimınatıng arbitfary log z=a log x+ V1-a' log y+ b

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Q: 3 [og,x + logy] – 2[log,a + log, V5]

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Q: Q1:B. Find the solution for x: log (væ+1+1) 3 log Vr – 40

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Q: Express as a single logarithm. 3 log bt- log bS O A. log t° + log s О В. Тoд b Oc. log, (° -s) 3t O…

A: Use the exponent rule of logarithm to write 3 as exponent.

Q: Differentiate the function T(z) = 2z log2 z.

A: The given function is,

Q: Compute 3 In(e) +2 log(10) 7 11 1 9. 3. B8

A: Solve by properties of logarithm.

Q: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,…

A: Explanation of the answer is as follows

Q: 19. f(x) = log,(7)* 20. f(x) = xlog101000 %3D

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Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

Q: d -log(z) = dz z O O 2- 1

A: We need to differentiate the function log(z) with respect to z. Differentiation is the process of…

Q: (B) 3log,(x)-4 log,(y) – log, (z)

A: The detailed solution is as follows below:

Q: Rearrange this equation to isolate A. H = K + log A =

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

Q: Express th equation in exponential form.

A: (a) Given expression is log35=x. Express the above equation in exponential. logab=c, then…

Q: Use log, 3 z 0.5869 and log, 5 z 0.8598 to find an approximate value for V5 logb 9

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Q: Use values of f(x) = In(x) %3D to estimate log ( 6.67 ) using 4th order

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

A: Given: log4z3

Q: Let u = In a and v = In b. Write the expression in terms of u and v without using the logarithm…

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Q: t(z)= 2z log2z  , t '(z)?

A: