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2 years ago

Expand each logarithm. log₄5 x

Mathematics

1 answer:

Romashka [77]2 years ago

5 0

If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that $log_{a}b$ = $log_{x}b/log_{x}a$ . We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that $log_{a}b$ = log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

Learn more about base change theorem at brainly.com/question/14998693

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3 years ago

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olga2289 [7]

Answer:

460 ft^2 of carpet will be replaced

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You need to find the area of the room and then take away the area of the six bookcases

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3 years ago

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$