Find the domain of f(x) = log(x^2-3)

Q: Show that loga 12x + 2x - 12 + loga 12x - 2x - 12 = 0.

A: given :                      loga (12x+2x-12) + loga(12x-2x-12) = 0 The product rule for logarithms…

Q: State the Chain Rule version of the derivative of the natural logarithmic function in your own…

A: The derivative of the composite function is known as chain rule in calculus. Consider the natural…

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

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Q: How is the natural logarithm function defined as an integral? What are its domain, range, and…

A: Explanation:

Q: Find the First Derivative: y=log10(5x+3/5x-4)

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Q: Give 1 problem for differentiation rule of exponential

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Q: Solve for x: log(5x + 45) – logx = 1

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: Show that 1 <x- log (1+x) < if - 1<x<0. 2 (1+x)

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Q: . Show that log(1) = 2nti, n = 0, ±1, ±2, ...

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Q: Find the limit of: limit of log5(8x-x4) as x approaches 2- (Use left hand limit)

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Q: Solve for : log(x + 5) – log(x + 2) = 2

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Q: Use the same-derivative argument, as was done to prove the Product and Power Rules for logarithms,…

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Q: Differentiate: 4. y = 6* log7 x

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Q: Find the exact value of the logarithmic expression without using a calculator. (If not possible,…

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Q: use logarithmic differentiation to find the 1st derivative f(x)= x²(2x+3) (x²+1)*

A: given function  f(x)=x22x+3(x2+1)4

Q: What is the branch point of log(−2)?

A: Given expression is, log-2 Now, at the point z=-2 we can consider the path as a circle of radius R.…

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: Evaluate the integral ∫log2xdx.

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Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log9 x…

A: Use the log property to simplify the left side of the equation log9 x+3 log3 x=14. Use property…

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: Find the intervals in which ,* is increasing or decreasing logx

A: use the first derivative for finding increasing and decreasing intervals.

Q: x3tanx

A: Given that :   Integrate( x+logx-x3tanx)

Q: Is it possible for a logarithmic function to have a domain of (-∞,4)? Why or why not? Include an…

A: We have to find a log function which domain is (-∞,4)

Q: Differentiate  log(secx+tanx

A: To differentiate the function

Q: What is the first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

Q: Explain why. A HOW IS the graph of flt) = logyt related to th graph of glt) - 4*?

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

A: lnx y4z53 =lnx +ln y4z53 =lnx +ln y4z513  ln y4z513 =13ln y4z5 =13ln y4-ln z5 =134 ln y-5 ln z =4 ln…

Q: In x

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

A: Known fact:log mn=nlog mlog mn=log m-log nlog mn=log m+log n

Q: Find the limit of: limit of log5(8x-x4) as x approaches 2-

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Q: Estimate using the change of base formula.

A: We have to estimate the logarithmic expression using base change formula: log612 We know base change…

Q: Use a graphing device to find all solutions of the equation, rounded to two decimal places..³- - x =…

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

A: We have to express in terms of logarithms of x, y, z or w: log3xyz We know the properties of…

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

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Q: 5log(8)-1 log(x)

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Q: What is the derivative of: log x/(x+1)

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Q: Find the nth order derivative of the natural logarithm function y=lnx.

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Q: Use a linear approximation to estimate log10(10.5).

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Q: Differentiate log[log(sinx)]

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Q: Show that 3 logVx + 2 log x –; logx = 3 log x 2

A: Given equation is  3logx+2logx-12logx=3logx

Q: Give 5 example of integrals yielding natural log functions with solution

A: The integral examples are:

Q: what is intergral log x /x

A: WE HAVE TO INTEGRATE

Q: 1. Express logx m + log, n-Glogx m- log, n): as a single logarithm.

A: As per our guidelines we are supposed to answer only one question, kindly repost the remaining…

Q: Use logarithmic differentiation to evaluate ƒ′1x2.  ƒ1x2=11 + x22sin x

A: Given: fx=11+x22sinx

Q: Expand loge x in powers of (x- 1) and hence evaluate log, 1-1 correct to 4 decimal places.

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Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: Write the derivative of 7 log8(x)

A: We have to find the derivative of 7 log8(x).

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

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Q: what is the natural logarithm of 1/exy?

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Q: Use logarithmic differentiaion to evaluate f`(x) f(x) = (5x)^(ln 5x)

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