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3 years ago

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

You might be interested in

8x 3x=24 what does x equal

Debora [2.8K]

8x * 3x = 24

24x = 24

x = 1

5 0

3 years ago

A genetic experiment involving peas yielded one sample of offspring consisting of 437437 green peas and 129129 yellow peas. Use

navik [9.2K]

Answer:

The null hypothesis: $\mathbf{H_o: p=0.27}$

The alternative hypothesis: $\mathbf{H_1: p \neq 0.27}$

Test statistics : z = −2.30

P-value: = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27

Step-by-step explanation:

From the given information:

Let's state the null and the alternative hypothesis;

Since The claim is that 27% of the offspring peas will be yellow.

The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.

i.e

$\mathbf{H_o: p=0.27}$

The alternative hypothesis state that the proportion of offspring peas will be yellow is not equal to 0.27

$\mathbf{H_1: p \neq 0.27}$

<u>The test statistics:</u>

we are given 437 green peas and 129 yellow apples;

Hence;

$\hat p = \dfrac{x}{n}$

where ;

$\hat p$ = sample proportion

x = number of success

n = total number of the sample size

$\hat p = \dfrac{129}{437+129}$

$\hat p = \dfrac{129}{566}$

$\mathbf{\hat p = 0.2279}$

Now; the test statistics can be computed as :

$z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }$

$z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }$

$z = \dfrac {-0.043 }{0.01866} }$

z = −2.30

C. P-value

P-value = P(Z < z)

P-value = P(Z< -2.30)

By using the P-value method and the normal distribution as an approximation to the binomial distribution.

from the table of standard normal distribution

move left until the first column is reached. Note the value as –2.0

move upward until the top row is reached. Note the value as 0.30

find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of

z = -2.30

P- value = 2P(z ≤ -2.30)

P-value = 2 × 0.01072

P - value = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27

8 0

3 years ago

Once you have created both sets of numbers, complete the following tasks. In each task, make sure to clearly label which set you

scoray [572]

Answer:

what set of numbers??

you haven't provided any set of numbers

7 0

2 years ago

If the measures of the angles of a quadrilateral are in the ratio of 3 : 4 : 5 : 8, find the measure (in degrees) of each angle.

BabaBlast [244]

Answer:

sorry just came here for the points

Step-by-step explanation:

6 0

3 years ago

Convert 2FA.C8 base 16. express in Octal form, Quinary or pental form and Binary form

Sunny_sXe [5.5K]

Using base conversion method, 2FA.C8 base 16 can be expressed as:

1372.628 in octal
11022.3423120034 in pental
1011111010.11001 in binary

<h3>What is 2FA.C8 base 16 expressed in Octal form?</h3>

To express 2FA.C8 in octal form, it is first converted to a decimal form as follows:

where:

F = 15

A = 10

C = 12

2FA.C8 = 2 × 16^2 + F × 16^1 + A × 16^0 + C × 16^-1 + 8 × 16^-2

2FA.C8 = 762.7812510 in decimal.

Then, convert 762.7812510 to octal as follows:

First the integral part is converted to octal by repeated division by 8.
The fractional part is converted to octal by repeated multiplication by 8 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 8 = 95 remainder 2

95 / 8 = 11 remainder 7

11 / 8 = 1 remainder 3

1 / 8 = 0 remainder 1

762 = 1372

Then;

0.78125 × 8 = 6 + 0.25

0.25 × 8 = 2 + 0

0.78125 = 0.62

Therefore, 762.78125 in decimal = 1372.628 in octal

<h3>What is 2FA.C8 base 16 expressed in pental form?</h3>

To convert 2FA.C8 base 16 to pental form, we use its value in decimal for conversion.

2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to pental as follows:

First the integral part is converted to pental by repeated division by 5
The fractional part is converted to pental by repeated multiplication by 5 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 5 = 152 remainder 2

152 / 5 = 30 remainder 2

30 / 5 = 6 remainder 0

6 / 5 = 1 remainder 1

1 / 5 = 0 remainder 1

762 in decimal = 11022 in pental

Then 0.78125 to pental:

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

0.53125 × 5 = 2 + 0.65625

0.65625 × 5 = 3 + 0.28125

0.28125 × 5 = 1 + 0.40625

0.40625 × 5 = 2 + 0.03125

0.03125 × 5 = 0 + 0.15625

0.15625 × 5 = 0 + 0.78125

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

Thus, 0.78125 in decimal = 0.3423120034 in pental

Therefore, 762.78125 in decimal = 11022.3423120034 in pental.

<h3>What is 2FA.C8 base 16 expressed in Binary form?</h3>

To convert 2FA.C8 base 16 to binary form, we use its value in decimal for conversion.

2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to binary as follows:

First the integral part is converted to binary by repeated division by 2
The fractional part is converted to binary by repeated multiplication by 2 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 2 = 381 remainder 0

381 / 2 = 190 remainder 1

190 / 2 = 95 remainder 0

95 / 2 = 47 remainder 1

47 / 2 = 23 remainder 1

23 / 2 = 11 remainder 1

11 / 2 = 5 remainder 1

5 / 2 = 2 remainder 1

2 / 2 = 1 remainder 0

1 / 2 = 0 remainder 1

762 base 10 = 1011111010 base two

Then 0.78125 to binary:

0.78125 × 2 = 1 + 0.5625

0.5625 × 2 = 1 + 0.125

0.125 × 2 = 0 + 0.25

0.25 × 2 = 0 + 0.5

0.5 × 2 = 1 + 0

0.78125 base 10 = 0.11001 base two

Therefore, 762.78125 base 10 = 1011111010.11001 base two.

Learn more about base conversion at: brainly.com/question/17946394

4 0

2 years ago