log, (2') = 2

Q: Solve for x using sci notation x=log(y^5) ; if (log y) = 1.2 x 10^-4

A: We have to find value of x by using scientific notation.

Q: Solve for æ: log(x + 2) – log(x + 1) = 1 You may enter the exact value or round to 4 decimal places.

A: here we will solve for x,

Q: Express the quantity as a single logarithm. In 2 +In 27

A: Given,

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

A:

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

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

A:

Q: Express In(1+r²) +In r- In sin r as a singel logarithm.

A: Use property of log :→n ln(m) = ln(mn)→ln(m) + ln(n) = ln(mn)→ln(m) - ln(n) = lnmn

Q: Show that, log5 x can be expressed as 2 log, x, where b> 0.

A:

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: Expand into several logarithms: x² y? In z5

A: We need to expand the given logarithms into several logarithms lnx2y3z5

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

A: Given :            loga y5 w2x4 z3  To express loga y5 w2x4 z3 in terms of logarithms of x, y, z…

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

A:

Q: log(x³) dx

A: Consider the integral: ∫logx3xdx…

Q: Log(X^3Y^2Z^7)

A:

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

A:

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

A: Given logarithmic expression is log4xz. To express logarithms in terms of x, y, z or w. Solution: We…

Q: se-2 log table (printed in

A:

Q: Whats the integral of (log_base8(8x))/x dx?

A:

Q: Express in terms of sums and differences of logarithms. 8 In 3xy 8 In 3 3x°y

A:

Q: y = (cos(x²))* -2 Co:

A:

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: Choose the exponential form of the logarithmic equation log3 (7x + 6) = 3. %3| O 33 = (7x + 6)° O…

A: Option c is correct.

Q: Use the properties of logarithms to expand log (zy).

A: Properties of Logarithms :i) log(ab) = log(a) + log(b)ii) log(ab) = b log(a)

Q: Express log x Vy/z in terms of logarithms of x, y, and z.

A: Express log x4y2/z3 in terms of logarithms of x, y and z.

Q: 2 log, (x) = 2

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

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

A: We have to express in terms of logarithms: log4yx We know the property of logarithm,…

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

A:

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

A: The given expression is logax3wy2z4

Q: If logx = 4 and logy =7, then the value of -log is %3D xy

A: Given, logx = 4  and  logy = 7 We have to find the value of  -log1xy.

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: 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: Solve the following logarithmic equation: log2 (x – 3) + log2 x – log2 (x + 2) = 2. - -

A:

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

A:

Q: = log z in the regio

A:

Q: y = log2vx

A: Given, y=log2x

Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

A:

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: (b) Show that 1 1+ 2 tanh- (2) = ; log

A:

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

A:

Q: 2 In x + 3 In y – In z

A:

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

A:

Q: Express th equation in exponential form.

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

Q: What is the linear approximation of log base 5 x at x=5

A:

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

A: Given: log4z3

Q: Differentiate. y= log 7x dx log 7x=

A: y=log7xTo differentiate.

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

A:

Q: Express single logarithm: log; x + 2 log, y – 3 log; z as a

A:

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.