Rewrite the expressions in Exercises 5–8  in terms of exponentials and simplify the results as much as you can. 5. 2 cosh (ln x) 6. sinh (2 ln x) 7. cosh 5x + sinh 5x 8. cosh 3x - sinh 3x

Q: Prove the following: Simplify the following by using exponential form: *+ Sinhox

A: I have typed a in place of alpha.

Q: .Expand log (1 + sin x) in powers of z as far as the term in r.

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Q: Determine all values of In(-2 ln(i)).

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Q: How do I write the exponential function in the form f(t) = ab^t passing through points (-1, 2/5) and…

A: The solution of given problem is followed by

Q: Use the definition in terms of exponential functions to prove the following 2. sech(2x) 1-tanh?x %3D…

A:

Q: Find a formula for the exponential function passing through the points 3, 27 and (2,18) f(x) =

A: Given:

Q: a. If (ln x)/x = (ln 2)/2, must x = 2? b. If (ln x)/x = -2 ln 2, must x = 1/2? Give reasons for your…

A: Take a function y= 2lnx - x*ln2

Q: 9. Condense the expression 1. 3 ln x+-In In(x²-1)-In(x² +1). 2

A: We make the coefficients into exponents inside log

Q: Find the exponential equation in the form y=ab^x whose graph passes through the points ( -3,0.032)…

A: Solution: The objective is to find the exponential equation is of the form y=abx

Q: Obtain all values of ln (−4)

A: ln(-4)

Q: Express th equation in exponential form.

A: a). Given, lnx+1=2 The exponential form is, x+1=e2         ∵lnx=y⇒x=ey⇒x=e2-1

Q: Give five examples of exponential functions in the form f(x) = b* and f(x) = a · b° + h with its…

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Q: 7. Use linear approximation to approximate the value of log(99) without the need for a calculator.…

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Q: Find the exponential function y = ab whose graph passes through the points (3, 108). y = > Next…

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Q: e3+j4(3+ j4)5 log ji' sin(3 + j4) j2022

A:

Q: write the exponontial equation of the average CO2 in PPM using years after the chosen year as an…

A: To find an exponential equation (y=aebx) - using the Least square method. Let

Q: Evaluate the expression, ln (1/e2)  without using a calculator. If evaluation is not possible, state…

A: Evaluate: ln1e2

Q: Using the complex exponential function, Find integral e^(3x)*sin(2x)*x^7

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Q: onvert to an exponential equation. ln 44 = 3.7842

A: ln(44)=3.7842

Q: How do I write the exponential function in the form f(t) = ab^t for the points (-1, 3/2) and (3,…

A: To write the exponential function in the form f(t) = abt

Q: write as sum/difference of logathirims. express powers as factors.    log2 (xy^6 / z^2)…

A: Logarithm

Q: Find simpler expressions for the quantities ln (e2 ln x)

A: Given: y=lne2lnx we know that lnm.n=lnm+lnn

Q: 3. Solve the Natural Logarithmic Equation: Inx+ In(x – 2) = In 63. (**

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Q: Find the formula for an exponential function of the form f(x) = A · Bº that passes through the…

A: We get exponential function by putting  both the point one by one and then by solving thes two…

Q: Determine whether the following statement is true or false, and explain why. (ln 3)4 = 4 ln 3

A: We know that, ln an=n ln a ; n is an integer

Q: Determine if the given functions are LI or LD by computing the Wronskian : -2x Yi = e*,y2 = e*,y; =…

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Q: Find the formula for an exponential function of the form f(x) = A · Bª that passes through the…

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Q: Give five examples of exponential functions in the form f(x)=bx and f(x)= a*bP(x)+h with its domain…

A: we have to give five examples of exponential functions with its domain and range.

Q: Find the exponential functions of the form f(x) ab* that pass througl

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Q: Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much…

A: From the definition of the hyperbolic trigonometric function. sinhx=ex-e-x2coshx=ex+e-x2

Q: Log4(x2+8) using base e

A: Given  The logarithmic expression is Log4(x2+8) Change of base formula for log

Q: Write a few sentences describing the relationship between ex and ln x.

A: ex &  lnx are inverse functions of each other.It is like solving equation ex=c for x using…

Q: Solve for A: AR+AT=E

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Q: 1. Given that z=8-6i, write its exponential form. Round off decimal answers up to 3 decimal places.

A: Here, a=8b=6

Q: 17. The product rule does apply when multiplying exponential functions with sinusoidal functions.

A: Yes the product rule applies when multiplying exponential functions with sinusoidal functions

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: In arcsin x (V1-x²)arcsin x

A: Given:     ∫lnarcsinx1-x2arcsinxdx    =∫lnarcsinx1-x2arcsinxdx substitute…

Q: Integrate and simplify:

A: to find the indefinite integrals of the given functions

Q: A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)“ , wherez…

A:

Q: In x to show that In a loga x = Use the change of base formula loga x = x In a loga x dx dx In a In…

A: topic - derivative of logarithmic function

Q: Find a formula for the exponential function passing through the points (−2,48) and (2,3). f(x)=

A:

Q: Simplify e2 ln x. Express 5x using the base e

A: Given- e2lnx . To simplify- The above expression and express 5x using base e. Concept Used- elnx=x

Q: 16 24 8 log. Z. to

A: Given logay16z24x58

Q: Find a formula for the exponential function passing through the points (– 2, 250) and (1, 2) | f(x)…

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Q: 3. Solve the natural logarithmic equation. 3 In In x + In In 2 = 4

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Q: Use the properties of logarithms to write the expressions in Exercises 43 and 44 as a single term.…

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Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The principal value of tan- (2i) is :Select one 1 +i-log, 3 .a 1 log, 3+ i- .b 2 2 c. None of these…

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