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scoray [572]
3 years ago
15

Solve the logarithmic equation: x= log5 (1/625)=

Mathematics
1 answer:
Verizon [17]3 years ago
5 0
You can convert (1/625) to an exponent, and it would be ideal to have 5 as the base of it because you want your log base to cancel it out. what i usually do in this case is just test out 5^1, 5^2, etc until i find one that matches the number i need. in this case because the number you're trying to work with is a small fraction, you'll want to use NEGATIVE exponents so it'll create a fraction instead of a large whole number:

5^-1 = 1/5
. . . keep trying those. . .
5^-4 = 1/625

so, because they're equal to one another, it'll be waaay easier after you substitute 5^-4 in place of 1/625

x = log₅ 5⁻⁴

log base 5 of 5 simplifies to 1. subbing in the 5^-4 gets rid of the log for you altogether, and your -4 exponent drops down:

x = -4 is your answer

if the exponent dropping down doesn't make sense to you, you can think of it in another way:

x = log₅ 5⁻⁴

expand the expression so that the exponent moves in front of the log function:

x = (-4) log₅ 5

then, still, log base 5 of 5 simplifies to 1, so you're left with:

x = (-4)1 or x = -4
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Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a norm
Artemon [7]

Answer:

a) 0.5.

b) 0.8413

c) 0.8413

d) 0.6826

e) 0.9332

f) 1

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 6, \sigma = 0.2

(a) P(x > 6) =

This is 1 subtracted by the pvalue of Z when X = 6. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6-6}{0.2}

Z = 0

Z = 0 has a pvalue of 0.5.

1 - 0.5 = 0.5.

(b) P(x < 6.2)=

This is the pvalue of Z when X = 6.2. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

(c) P(x ≤ 6.2) =

In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.

(d) P(5.8 < x < 6.2) =

This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X  5.8.

X = 6.2

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 5.8

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

(e) P(x > 5.7) =

This is 1 subtracted by the pvalue of Z when X = 5.7.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

1 - 0.0668 = 0.9332

(f) P(x > 5) =

This is 1 subtracted by the pvalue of Z when X = 5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5-6}{0.2}

Z = -5

Z = -5 has a pvalue of 0.

1 - 0 = 1

5 0
3 years ago
GEOMETRY: Find JL of the line.
Yuliya22 [10]

Answer:

JL = 31

Step-by-step explanation:

JL is the total length of the line segment. We know that JK is 15 units long and that KL is 16 units long. So, you would add these numbers (15 & 16) together to get the total length of the line segment. Hope this helps! :)

6 0
3 years ago
In a ‘30% off’ sale, a hat was £101.50. Work out the original price
castortr0y [4]
Say the original price is x
x*[(100-30)/100]=101.50
now solve it
x= 101.50*100/70
8 0
3 years ago
What is the mode?<br> 0-0-2-1-3-2-1-0
exis [7]
The mode is 0 since it is the most frequent.
4 0
3 years ago
Read 2 more answers
Find the value of x that makes lines u and v parallel
gogolik [260]

Answer:

x = 4 for Lines U and V to be parallel

<u>Skills needed: HS Geo, Angle Theorems, Equations</u>

Step-by-step explanation:

1) We see that there are two angle measures given to us. There is an angle marked with the measure of 130°, and the other is marked with (33x-2)°.

  • First of all, these two angles are categorized alternate interior angles. They are on alternate sides of the transversal, and are within the two lines (not on the outer side of the lines). I will add an image for reference regarding this idea.
  • If 2 lines are parallel, alternate interior angles are congruent. This means that: 33x-2=130

2) Solving this equation is fairly straightforward.

  • 33x-2+2=130+2 (add 2 to both sides in order to get the 33x by itself.
  • 33x\div33=132\div33 (to get x by itself)
  • 132 divided by 33 is 4, and 33x divided by 33 is x, so x=4

--------------------------------------------------------------------------------------------------------------Hope you understood, have a great day.

7 0
2 years ago
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