1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mezya [45]
3 years ago
11

Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the

following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses
Mathematics
1 answer:
enyata [817]3 years ago
6 0

Answer:

<h2>24</h2>

Step-by-step explanation:

Given the following logarithmic expressions log_ax = 3, log_ay = 7, log_az = -2, we are to find the value of log_a(\frac{x^3y}{z^4} )

from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}Substituting x = a³, y = a⁷ and z = a⁻² into the log function log_a(\frac{x^3y}{z^4} ) we will have;

= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24

Hence, the value of the logarithm expression is 24

You might be interested in
Which statement correctly compares the function shown on this graph with the function y = -x+ 4?
s344n2d4d5 [400]

Answer:

I think the answer for this question is C

6 0
3 years ago
Read 2 more answers
4.89; 4.089; 4.870; 4.881 - Put these in order from least to greatest. Your answer​
motikmotik
Answer: 4.089; 4.870; 4.881; 4.89
3 0
2 years ago
Read 2 more answers
NEED HELP FAST! WILL GIVE POINTS AND BRAINIEST!!
icang [17]
W=15 no

W= 21 no

W= 1 Yes

If im right the question is just asking which variable is less than 15. 
so the only variable that is less than 15 is 1.
7 0
3 years ago
Read 2 more answers
Using the quadratic formula to solve 11x²-4x=1 What are The values of X?
Anvisha [2.4K]
11x^2 - 4x = 1
11x^{2} - 4x - 1 = 1 - 1
11x^{2} - 4x - 1 = 0
x = \frac{-(-4) \± \sqrt{(-4)^{2} - 4(11)(-1)}}{2(11)}
x = \frac{4 \± \sqrt{16 + 44}}{22}
x = \frac{4 \± \sqrt{60}}{22}
x = \frac{4 \± 2\sqrt{15}}{22}
x = \frac{2 \± \sqrt{15}}{11}
x = \frac{2 + \sqrt{15}}{11}\ \bold{or}\ x = \frac{2 - \sqrt{15}}{11}
8 0
3 years ago
Read 2 more answers
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig
Keith_Richards [23]

Answer:

1. Null hypothesis: \mu_{A}=\mu_{B}=\mu_{C}

Alternative hypothesis: Not all the means are equal \mu_{i}\neq \mu_{j}, i,j=A,B,C

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: \mu_{A}=\mu_{B}=\mu_{C}

Alternative hypothesis: Not all the means are equal \mu_{i}\neq \mu_{j}, i,j=A,B,C

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have p groups and on each group from j=1,\dots,p we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

And we have this property

SST=SS_{between}+SS_{within}

We need to find the mean for each group first and the grand mean.

\bar X =\frac{\sum_{i=1}^n x_i}{n}

If we apply the before formula we can find the mean for each group

\bar X_A = 27, \bar X_B = 24, \bar X_C = 30. And the grand mean \bar X = 27

Now we can find the sum of squares between:

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

Each group have a sample size of 4 so then n_j =4

SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72

The degrees of freedom for the variation Between is given by df_{between}=k-1=3-1=2, Where  k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306

And the degrees of freedom are given by:

df_{within}=N-k =3*4 -3 = 12-3=9. N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34

C. 34

Part 4

The test statistic F is given by this formula:

F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is F_{crit}=8.02

B. 8.02

5 0
3 years ago
Other questions:
  • Please help need help
    10·2 answers
  • Find the surface area of the sphere shown r=2 please show work
    9·1 answer
  • Which point is on the line, y=4x+2?
    7·1 answer
  • Which of the following is a factor of 2x2–7x–15?
    13·1 answer
  • A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equati
    11·1 answer
  • A ball is drawn at random from a box containing 6 red balls, 4 white balls and 5 blue
    12·1 answer
  • What happens to the value of the expression c + 2 as it increases?
    12·1 answer
  • Join meh classroom please (you're joining Hogwarts btw)
    10·1 answer
  • What is 26 out of 100 expressed as a ratio in simplified form?
    15·2 answers
  • Lincoln is preparing many gifts for a family holiday party. Each gift must either be wrapped with wrapping paper or prepared in
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!