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kvv77 [185]
3 years ago
6

Evaluate the expression. If necessary, round to the nearest hundredth. log 4 64

Mathematics
2 answers:
grigory [225]3 years ago
8 0
<span>log 64 base 4 = 3

properties of log:
log a base b = x   >>>   b^x = a

so </span>log 64 base 4 = 3 >>> 4^3 = 64 

or 64^(1/3) = 4 
Allushta [10]3 years ago
6 0
The correct answer is: 3
Explanation:


Instead of sharing the conventional tedious, method, let me share with you the simple trick here to solve these types of questions without using the calculator:

Given
log_464

It is essentially saying that WHAT power of 4(which is the base of log) gives us the value 64. You need to find the answer to that "WHAT."

Well

4^1 = 4 \\&#10;4^2 = 16 \\&#10;4^3 = 64

Hence the answer is "3".

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3 determine the highest real root of f (x) = x3− 6x2 + 11x − 6.1: (a) graphically. (b) using the newton-raphson method (three it
Juliette [100K]

(a) See the first attachment for a graph. This graphing calculator displays roots to 3 decimal places. (The third attachment shows a different graphing calculator and 10 significant digits.)

(b) In the table of the first attachment, the column headed by g(x) gives iterations of Newton's Method. (For Newton's method, it is convenient to let the calculator's derivative function compute the derivative f'(x) of the function f(x). We have defined g(x) = x - f(x)/f'(x).) The result of the 3rd iteration is ...

... x ≈ 3.0473167

(c) The function h(x₁, x₂) computes iterations using the secant method. The results for three iterations of that method are shown below the table in the attachment. The result of the 3rd iteration is ...

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(d) The function h(x, x+0.01) computes the modified secant method as required by the problem statement. The result of the 3rd iteration is ...

... x ≈ 3.0477377

(e) Using <em>Mathematica</em>, the roots are found to be as shown in the second attachment. The highest root is about ...

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_____

<em>Comment on these methods</em>

Newton's method can have convergence problems if the starting point is not sufficiently close to the root. A graphing calculator that gives a 3-digit approximation (or better) can help avoid this issue. For the calculator used here, the output of "g(x)" is computed even as the input is typed, so one can simply copy the function output to the input to get a 12-significant digit approximation of the root as fast as you can type it.

The "modified" secant method is a variation of the secant method that does not require two values of the function to start with. Instead, it uses a value of x that is "close" to the one given. For our purpose here, we can use the same h(x1, x2) for both methods, with a different x2 for the modified method.

We have defined h(x1, x2) = x1 - f(x1)(f(x1)-f(x2))/(x1 -x2).

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3 years ago
How do you find the lateral area of a pentagonal prism?
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3 years ago
A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b what is the length of the third side ?
RideAnS [48]

Answer:

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Step-by-step explanation:

The perimeter is the sum of the lengths of the three sides. If x represents the length of the third side, then ...

  (3a +8) +(5a +b) +x = (10a +3b +12)

Subtracting from the equation everything on the left side that is not x, we get ...

  x = (10a +3b +12) -(3a +8) -(5a +b)

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5 0
3 years ago
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zlopas [31]

Answer:

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(6.253•10^-2)(7.112x10^3)

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Six years less than Tracy's age write it as a algebratic expression
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