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podryga [215]
3 years ago
14

Rewrite the equation in logarithmic form: 2³= 8

Mathematics
2 answers:
elena55 [62]3 years ago
7 0

Answer:

3 log 2 = log 8

Step-by-step explanation:

Take the log of both sides of the given equation 2^3 = 8:

log 2^3 = log 8, which simplifies to 3 log 2 = log 8.

This is equivalent to the given 2^3 = 8.

Instead of the common log, you could also use the natural log, "ln."

Alternatively, use the base-2 log:

2^3 = 8

Taking the base-2 log of both sides, we get 3 = log-2 of 8  = 3

GrogVix [38]3 years ago
6 0

Explanation: The base of the power in the original equation becomes the base of the log. So we have ^{log}2. Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the original equation goes inside the log.

So we have ^{log} 2 8 = 3 which is 2³ = 8 written in logarithmic form.

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The price of a computer component is decreasing at a rate of 15% per year.
Alex_Xolod [135]

Answer:

  • exponential
  • $30.71

Step-by-step explanation:

Usually, this wording means the decrease is proportional to the current price, characteristic of an exponential function.

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The decay factor is 1-(decay rate), so is 1-0.15 = 0.85. After 3 years, the value has been multiplied by this factor 3 times:

  $50×0.85³ ≈ $30.71 . . . . cost in 3 years

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<em>Comment on percent per year</em>

Less often, the indicated decrease is intended to be <em>that percentage of the original price</em>. The result is that the price decreases by a constant amount each year, a linear decrease. This condition most often arises in conjunction with figuring depreciation in value for tax or accounting purposes.

The upshot is that you always need to be careful to understand what the base of a percentage is intended to be.

5 0
3 years ago
The graph of f(x) = 2x^2 + 20x + 48 is shown
Free_Kalibri [48]

Answer:

a) The equation in intercept form by factoring is (x+6)(x+4)

b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.

c) The solutions of  2x^2+20x+48=0 is (x+6)(x+4)=0 that is x= -6 and x = -4.

Step-by-step explanation:

The given quadratic  equation is f(x)=2x^2+20x+48

Put the function f(x) = 0 , then f(x)=2x^2+20x+48=0

a) The equation in intercept form by factoring is ,

Consider the given function,

f(x)=2x^2+20x+48=0

\Rightarrow 2x^2+20x+48=0

taking 2 common, we get,

\Rightarrow 2(x^2+10x+24)=0

\Rightarrow x^2+10x+24=0

The above is a quadratic equation of the form ax^2+bx+c=0

Solving quadratic equation using middle term splitting method,

\Rightarrow x^2+6x+4x+24=0

\Rightarrow x(x+6)+4(x+6)=0

\Rightarrow (x+6)(x+4)=0

Thus, The equation in intercept form by factoring is (x+6)(x+4).

b) From the given graph x- intercepts are (-4,0) and (-6,0) .

Zeroes / roots of a function are those points where the value of the function is zero.

Put f(x) = 0  as solved above

that is (x+6)(x+4)=0

\Rightarrow (x+6)=0 or \Rightarrow (x+4)=0

\Rightarrow x=-6 or \Rightarrow x=-4

Thus, zeros (roots) of the function are -6 and -4.

For checking put x = -6 and -4 in the function we get f(x) =0 .

c) The solutions of  2x^2+20x+48=0 is (x+6)(x+4)=0 that is x= -6 and x = -4 as shown above.


8 0
3 years ago
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