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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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Jonah drives from his car to and from work. The total length of the trip to and from work is 19.2 miles. In August, Jonah worked
natita [175]
ANSWER

The total length of the trip to and from work in August is

403.2 \: miles

EXPLANATION

The total length of the trip to and from work is

19.2 \: miles

If Jonah worked 21 days in August,

Then, the total length of the trip to and from work is
= 21 \times 19.2 \: miles

Change the decimal to fraction and multiply,

= 21 \times \frac{192}{10} miles

= \frac{21 \times 192}{10}

= \frac{4032}{10} miles

Convert back to decimal

= 403.2 \: miles
6 0
3 years ago
Write the following equation in the general form Ax + By + C = 0 <br> 2x + y = 6
ki77a [65]
The Answer is 2x + Y - 6 =0
5 0
3 years ago
Watch help video
Evgen [1.6K]

Answer:

20 dimes and 2  quarters

Step-by-step explanation:

x = number of dimes

y  = number of quarters

minimum is greater than or equal to ≥

x+y ≥16

no more than is less than or equal to ≤ ,

value of dime is $ 0.10

value of quarter is $0.25 so

0.10x + 0.25y ≤ 3.00

Rewrite inequalities in terms of y:

y ≥16 - x

(0.25/0.25)y ≤ (3.00/0.25)-(0.10/0.25)x→

y≤12 - 0.4x

Graph system: see file

6 0
3 years ago
I already solved this but I'm confused if the answer is A or C?
irinina [24]
The answer is C. a 4.5 feet, b. 30 feet
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