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Masja [62]
3 years ago
13

how to solve for 8^x=2 (I know the answer is 1/3 but i have to show work and i don't know the process to solve it)

Mathematics
1 answer:
Lunna [17]3 years ago
5 0

Answer:

  x = 1/3 . . . . math facts or logarithms are involved; take your pick

Step-by-step explanation:

When you are solving for a variable that is in an exponent, logarithms are often useful. Taking the log of both sides of this equation, you have ...

  log(8^x) = log(2)

Using the rules of logarithms, that is ...

  x·log(8) = log(2)

  x = log(2)/log(8) . . . . . divide by the coefficient of x

You can find the value of this on your calculator, and it will tell you the value is  0.333333333333 or as many digits as your calculator displays. That is a clue that the exact answer is probably 1/3.

__

You should recognize that 8 = 2·2·2 = 2^3, so log(8) = 3log(2) and the above solution becomes ...

  x = log(2)/(3log(2)) = 1/3

__

Recognizing that 8 = 2^3, you can make that substitution into the original equation to get ...

  (2^3)^x = 2

  2^(3x) = 2^1

  3x = 1 . . . . . . . matching exponents; equivalent to taking logs base 2

  x = 1/3 . . . . . .  divide by 3

__

All of the above using 2 as a base of exponents is just dancing around the fact that you already know the math fact ...

  8^x = 2 = 8^(1/3)

  x = 1/3 . . . . . equating exponents; equivalent to taking logs base 8

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If you want the subtraction also done its 1 4/10.
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Match the phenomenal expression on the left with the simplified version on the right
nalin [4]

Given the polynomial expression:

(y + 5)²

(y - 5)(y + 5)

Let's simplify each of the given expression:

a.) (y + 5)²

The given equation is a factor of a perfect square trinomial. For this type of expression, the following is the formula for expanding it.

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We get,

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We get,

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8 0
1 year ago
If you go out to eat with 3 friends and your meal was $72.50, what should you leave for gratuninty if you want to tip your waite
kvv77 [185]

Answer:

$10.88 or round up to $11

Step-by-step explanation:

Since 15 is expressed as a percent, you can convert it to a decimal.

.15, which can also be 15/100 if you were to write it as a fraction.

You are trying to find 15% of 72.50 so you would need to multiply your new decimal (.15) to your meal total. This will give you 10.875 or 10.88.

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Let the current speed be c.
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The speed going downstream is 32/4 = 8 mph.
b - c = 5 ........(1)
b + c = 8 .......(2)
Adding equations (1) and (2) we get:
2b = 13
b = 13/2 = 6.5
Plugging in the value for b into equation (1) we find c = 1.5.
The boat speed in still water is 6.5 mph and the current speed is 1.5 mph.
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