For a certain constant a 7 1, ln a ≈ 3.8067. Find approximate values of log2 a and loga 2 using the fact that ln 2 ≈ 0.6931.

Q: Given that log x= 4 and log y = 1.5 , find the value of log (x²y)

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Q: dy (x² + 1)? if y = 2) Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A: Here we have to find the the derivative of y

Q: The perception of the loudness B (in decibels, dB) of a sound with physical intensity I (in W/m²) is…

A: we use  Logamn = nLogam  Logaa = 1

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

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Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D = 10 log, where I is…

A: Question 19 - Equation to calculate loudness of sound in decibels-D = 10logII0…

Q: Use the properties of logarithms to approximate the indicated logarithms, given that ln 4 1.3863 and…

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Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D = 10 log, where I is…

A: Given: I=1012I0

Q: Evaluate / dx (x+2)²–49 O None to log() x-5 x+3 log() -5 x+7 ts log() x-5 x+9

A: We have to evaluate: ∫dxx+22-49

Q: The loudness ‘L’ of sound (sound level) in dB, with intensity ‘I’ in watts per square metre (W/m^2)…

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Q: 2- for y = log10 e" is: dx 1 1 a) *In 10 b)- *In 10 10 In e

A: Option (a) is correct. For detail....go through the solution

Q: For f(z) = 3e7'the value of log(f(z)) is

A: Given,       f(z)=3eπ6i

Q: Consider the following. e0.6x = 8 %3D (a) Find the exact solution of the exponential equation in…

A: Apply ' ln ' on both sides

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A: We will use the given decay function and initial conditions to find the require time

Q: . Given x = 22 log3 (9) , what goes in the blank of y

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Q: Find simpler expressions for the quantities 2 ln√e

A: 2 ln√e We need to simplify the given expression.

Q: Suppose that the sound at a rock concert measures 124 dB (decibels). a. Use the formula L = 10 log…

A: Part (a) - Loudness of sound = L = 124 dBInitial intensity of sound = I0 = 10-12 W/m2Final intensity…

Q: The sales of a new product ( in items per month) can be approximated by the following formula, where…

A: We need to find S(33). S(33)=325+500log(100)

Q: What is the increase in decibels when an artist doubles the intensity of a particular sound in a…

A: Given : L(I) = 10[ log(I/I_0)] When intensity increases to double I' = 2I

Q: If log4 x=3and 20+3y=101, find the numerical value of xy in simplest form

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Q: For Exercise, solve for the indicated variable. M = 8.8 + 5.1 log D for D

A: Consider the provided equation,

Q: The magnitude of an earthquake, R is defined by R log10 where I, is the intensity of the earthquake…

A: Please rate

Q: By using natural logarithm (ln), find dy/dx for this equation, 384=(x+2)3/4(y+3)1/3.

A:

Q: On the Richter scale, the magnitude, R, of an earthquake of intensity I is given by R = log (I/I0) ,…

A: Given: R=logII0 for finding intensity of an earthquake in Richter scale, we substitute intensity…

Q: The magnitude of an earthquake is measured on the Richter scale using the formula I R(1) = log -…

A: This is logrithmic with base 10.  Put R(I) = 5.8 and take anti logrithmic.

Q: (d) Solve the following equations for x. (Correct to 4 decimal places) (i) 2ex-1 = 4 (ii) log5 x –…

A: Brief answer is given below.

Q: 1. Solve for the following for x: Log6(x+2) = 2

A: We have to solve

Q: Find the solution for x: log (vz+1+1) log Vz- 40

A:

Q: Based on the data for the year of 1910 to 2007, the expected lifespan of people and country a can be…

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Q: Find x rounded to three decimal places. (1)log(3æ +2) = log(2a + 5) (2)log a – log 5 = log 7 2…

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Q: Find the value(s) of x for which the equation is true. log(x + 3) = log x + log 3

A: We have to find the value of x for the given equation: logx+3=logx+log3 We know the properties of…

Q: A person places $419 in an investment account earning an annual rate of 9.2%, compounded…

A: Given that P= principal initially invested=$419 annual rate = r =9.2%=0.092 Time=t =20 years find…

Q: About how many times more intense is an earthquake that measures 8.3 on the Richter scale than an…

A:

Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D= 10 log (1/1,), where…

A: D=10(logI-logI0)=10logII0 Where I= intensity of the sound in watts per square meters I0=intensity of…

Q: The loudness of sound (L, measured in decibels) perceived by the human ear depends on intensity…

A:

Q: Find derivative for the following exponential function at x = 0 e(x²-e5*) O -5 e O -5/e O 5e O 5/e

A: We know ddxef(x) = ef(x)·f'(x)

Q: Solve the following equation using the natural logarithm. Round answer to the nearest thousandth.…

A: Given that       2ln(3)+ln(x+6) = ln(90)

Q: Consider the following. 4x/12 = 0.9 E (a) Find the exact solution of the exponential equation in…

A: We have to solve

Q: log x is the exponent to which the base 10 must be raised to get. So we can complete the following…

A: The given statement is  log x is the exponent to which the base 10 must be raised to get _____   log…

Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

A:

Q: For which value of x is the equation true? 10* = 2e %3D 1+ln 2 In 10 In 10 O 1+log2

A: Given, The equation  10x = 2e  We have to find the value of x for which the equation is true.

Q: If a population grows exponentially at a rate r, the time it will take for the population to double…

A: We can derive the formula for the time it will take for the population to double using the basic…

Q: Suppose that at time t =0, half of a “logistic” population of 100;000 persons have heard a certain…

A:

Q: If f(x) = log; (4 + e ), then f' (x) equals et а. (4+ e² ) ln(3) b. 1 (4+ e²² ) ln(3) 2xe22 С. (4 +…

A: We will use property of logarithm and chain rule of derivatives

Q: If f(x)= log x , then f"(1) equals 1 (d) In 10 1 (a) 1 (b) 0 (c) -1 (e) In 10

A: We are given that f(x)=log x. So,            f''(x)=log10x''         =1xln10'         =-1ln10x2 Now,…

Q: For a X2 equals to 20, compute and compare the values of Y for log(X1) equals to 0.250 and 0.500.…

A: Given: logY=-0.6838+0.5921*logX1+0.0394*X2

Q: The decay of 713 mg of an isotope is given by A(t) = 713 e 0.029t wheret is time in years. Find the…

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Q: i. Solve for x: a) 32x-5 = 27 b) log x = log 3 + 2 log 4 ii. If RM 400 is invested for 2…

A: here solve for x a) 32x-5 = 27      32x-5 = 33     here 27 = 33    so now     2x - 5 = 3…

Q: A person places $123 in an investment account earning an annual rate of 2.8%, compounded…

A: Explanation and solutions is given below....