What is the increase in decibels when an artist doubles the intensity of a particular sound in a recording studio? Use the fact that loudness (L(1)) in decibels is related to intensity of sound (I) by the following: L(1) = 10 [ log (1/I_0)] where I_0 is the intensity of a barely audible sound

Q: How do I change y = log 3 below (x-3) to exponential form

A: If c=logbaSo, bc=a

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

Q: What is the decibel level of the noise from a motorcycle with intensity 10−2 watts per square inch?…

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Q: Use the properties of logarithms to expand the logarithmic expression.

A:

Q: Solve th equation for x. log2(log3 x) = 4

A: Consider the given: log2log3x=4Using log Rule:logap=n is equivalent to p=an,log2log3x=4…

Q: 6. Condense the logarithmic expression 2 lnx- In(x* +1).

A:

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: . How is the graph of log x related to the graph of ln x?

A: Here , ln x represents the natural logarithm where its base is e whereas the base of log x is 10 .…

Q: Differentiate the Logarithmic function: y = 3 ln square root of x

A:

Q: In(x-글) + In(2) = 2 In(x)

A: Please refer the attached image for complete solution. THANK YOU.

Q: express the numbers in terms of natural logarithms. tanh-1 (-1/2)

A: We will use the formula

Q: The derivative of an exponential function isn't always another exponential function.

A: Derivative of an exponential function is given by :ddxef(x,y,z) = ef(x, y , z). ddxf(x, y , z)

Q: Compute log3 without using a calculator, where log3(X) = 81 - 1.5

A: Using logarithmic Properties.

Q: Solve for x: 9. -log3 x = – 10 = x You may enter the exact value or round to 4 significant decimal…

A: Given:       95log3x=-10

Q: Express log (x + 1)³ – 2log (x + 1) + 3 log (x – 1)²– log (x³ – 1) as a single logarithm

A: Logarithmic equation: A logarithmic equation is an equation involving the logarithm of an expression…

Q: Express sinh-1 x in terms of logarithms.

A: Let  y=sinh-1x⇒x=sinhy

Q: (a) In (x (b) log; 2y2

A:

Q: =xpress the number sinh in terms of natural logarithms- 84 -

A: Given: sinh-1-1384

Q: Express in terms of logarithms without exponents. logb(x3y9z) What is the equivalent expression?…

A:

Q: Use logarithmic properties to write in simpler form. In xy In xy =

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Q: b- find x for following 1. logx = V2 2.ln(x + 1) = 5

A:

Q: Write 5 ln x + 3 ln (x² + 4) – , In (x + 8) single logarithm. as a - -

A: The logarithmic expression is given by 5ln(x) + 3lnx2+4 - 12lnx+8

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

A:

Q: a. find x from the equation log2 x=2 b. find x from the eqaution logx 3=2

A: Given, a. find x from the equation log2 x=2 b. find x from the eqaution logx 3=2

Q: Express the quantity as a single logarithm.

A: Given 13lnx+23+12lnx-lnx2+3x+22 The properties of logarithm used here are…

Q: Differentiate log sin x by first principles.

A:

Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

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

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Q: Differentiate: 3. y = log₂ (x¹ - x)

A: y = log9(x4 -x) here logerithmic function is given  dlogax/dx = 1/x(lna) use this formula and chain…

Q: What are some of the important characteristics of exponential functions?

A: We need to mention some characteristics of the exponential function. Let's begin.

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

A:

Q: How is loga x defined?

A: The logarithmic function y=logax is defined to be equivalent to the exponential equation x=ay. Here,…

Q: what is an exponential function?  Is it continuous?

A: what is an exponential function?  Is it continuous?

Q: Which grows faster In(x) or log (x)

A: ln(x) grows faster than log(x) Look for the graph using Desmos graphing calculator.

Q: Use the properties of logarithms to expand the logarithmic expression.      ln(xyz)

A: Given: ln xyz To expand: The given logarithmic function.

Q: Why is  the logarithmic function  not defined for negative values of x, thesoftware can produce only…

A: The definition of logarithmic function is, logbx=y⇒by=x The output value of exponential function by…

Q: Use the power rule to expand the logarithmic expression: ln √x

A: Given: lnx

Q: Use the power rule to expand the logarithmic expression: ln 3√x

A:

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: solve for x, log(x+5)-log(x+2)=2 please show work.

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Q: 2 In x + 3 In y – In z

A:

Q: Differentiate y = - using Logarithmic differentitation. A x2x' +1

A: Given;  y=ecosx^2/[pi x sqrt(2x3+1)].

Q: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

A:

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

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Q: Solve for x given: log2(x + 7) − log2(2x) = 3

A: The given logarithmic function is log2(x+7)-log2(2x)=3

Q: The count in a bacteria culture was 600 after 15 minutes and 16054 after 35 minutes. Assume that…

A: Given that      The count in a bacteria culture was 600 after 15 minutes and 16054 after 35 minutes.…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.