All categories

3 years ago

If log 2^x = log 3, then which is the value of x?

Mathematics

1 answer:

natulia [17]3 years ago

8 0

There's a property of logs I want you to remember, that is:

log(a)ᵇ = b*log(a)

We'll be using this property to solve the question

Finding x:

log(2)ˣ = log(3)

x*log(2) = log(3) [using the property mentioned above]

x = log(3) / log(2) [dividing both sides by log(2)]

Hence, the correct answer is option E.

You might be interested in

The prime factorization of 16x5

RoseWind [281]

Answer:

well first 16x5=80

2 * 2 * 2 * 2 * 5

Step-by-step explanation:

Hope that helps! :)

6 0

3 years ago

A right prism with rhombus bases is shown. The side length of each rhombus is 5 units. The height of the prism is 16 units. The

Papessa [141]

Volume of the prism:
V = B · h, where B stays for the area of the base and h stays for the height of the prism. And we know that d1 = 8, d2 = 6
B = ( d1 · d2 ) / 2 = ( 8 · 6 ) / 2 = 48 / 2 = 24
V = 24 · 16 = 384
Answer:
The volume of the prism is 384 cubic units.

5 0

3 years ago

Read 2 more answers

Latrell and his cousin, Tisha, met at a state park to go for an all-day hike. Latrell drove 122 miles to get to the park, and it

Naddika [18.5K]

Answer:

3 miles

Step-by-step explanation:

122/2 is 61

64 plus 32 is 96. 96/1.5 is 64 meaning that she goes 64 miles an hour.

so she goes 3 miles faster on average than latrell, with latrell going 61 an hour average and her going 64 an hour average

5 0

2 years ago

Read 2 more answers

Breyers is a major producer of ice cream and would like to test if the average American consumes more than 17 ounces of ice crea

asambeis [7]

Answer:

The conclusion for this hypothesis test would be that the average American consumes less than or equal to 17 ounces of ice cream per month.

Step-by-step explanation:

We are given that Breyers is a major producer of ice cream and would like to test if the average American consumes more than 17 ounces of ice cream per month.

A random sample of 25 Americans was found to consume an average of 19 ounces of ice cream last month. The standard deviation for this sample was 5 ounces.

Let $\mu$ = average ounces of ice cream consumed by American per month

So, Null Hypothesis, $H_0$ : $\mu \leq$ 17 ounces {means that the average American consumes less than or equal to 17 ounces of ice cream per month}

Alternate Hypothesis, $H_A$ : $\mu$ > 17 ounces {means that the average American consumes more than 17 ounces of ice cream per month}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average = 19 ounces

s = sample standard deviation = 5 ounces

n = sample of Americans = 25

So, test statistics = $\frac{19-17}{\frac{5}{\sqrt{25} } }$ ~ $t_2_4$

= 2

The value of the test statistics is 2.

Now at 0.025 significance level, the t table gives critical value of 2.06 at 24 degree of freedom for right-tailed test. Since our test statistics is less than the critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the the average American consumes less than or equal to 17 ounces of ice cream per month.

8 0

3 years ago

What are the first five sequences to the equation f(1)=2/3,f(n)=f(n-1)x3/2

iren [92.7K]

Answer:

2/3,1,3/2,9/4,27/8

Step-by-step explanation:

f(1)=2/3

f(n)=f(n-1)×3/2

f(2)=f(2-1)×3/2=f(1)×3/2=2/3×3/2=1

f(3)=f(3-1)×3/2=f(2)×3/2=1×3/2=3/2

f(4)=f(4-1)×3/2=f(3)×3/2=3/2×3/2=9/4

f(5)=f(5-1)×3/2=f(4)×3/2=9/4×3/2=27/8

7 0

3 years ago