All categories

3 years ago

Find log_{3} [27*\sqrt[4]{3} ] wihout using a calculator. Please show all work!

1 answer:

4 0

$\bf \textit{logarithm of factors}
\\\\
log_a(xy)\implies log_a(x)+log_a(y)\\\\
-------------------------------\\\\
log_3(27\sqrt[3]{3})\qquad 
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
\sqrt[3]{3}=\sqrt[3]{3^1}\\
\qquad 3^{\frac{1}{3}}
\end{cases}\implies log_3\left( 3^3\cdot 3^{\frac{1}{3}} \right)
\\\\\\
log_3\left( 3^{3+\frac{1}{3}} \right)\implies log_3\left( 3^{\frac{4}{3}} \right)\implies \cfrac{4}{3}\cdot log_3(3)\implies \cfrac{4}{3}\cdot 1\implies \cfrac{4}{3}$

You might be interested in

An investment advisor believes that there is a 60% chance of making money by investing in a specific stock. If the stock makes m

inessss [21]

Answer:

$\mathbf{ 0.6 \times 0.5 = 0.3 }$

Step-by-step explanation:

Let M denote the event that the stock makes money and D denote the event that the stock pays dividends.

It is given that $P(M) = 0.6$

Observe that the two events M and D are not independent because if the stock doesn't make money then it will not pay dividends. Therefore the event $D | M^{c}$ (D given M does not occur) is a null event, i.e

$P(D|M^{c}) = 0$

It is also given that,

$P(D|M) = 0.5$

Recall that : $P(D|M) = \frac{P(D \cap M)}{P(M)}$

Here, we are required to find $P(D \cap M)$

$P(D \cap M) =P(D|M) \times P(M)= 0.5 \times 0.6 = 0.3$

7 0

3 years ago

Washington (CNN) About three-quarters of Americans (77%) approve of President Donald Trump's decision to meet with North Korean

snow_tiger [21]

Answer:

b. The margin of error would decrease.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

$M = z\frac{\sigma}{\sqrt{n}}$

In which z is related to the confidence level, $\sigma$ is the standard deviation of the population and n is the size of the sample.

This means that the margin of error is inversely proportional to the size of the sample, which means that if the sample size increases, the margin of error decreases.

In this question, the sample size is increased, leading to a smaller margin of error. So the correct answer is given by option b.

8 0

3 years ago

Please right answer for 25 pts and a mark. A store is having a sale on chocolate chips and walnuts. For 3 pounds of chocolate ch

Alexxandr [17]

Answer:

Chocolate Chips are 1.50 per pound and Walnuts are 3.25 per pound.

3 0

3 years ago

Write the equation of a line in point-slope form that goes through the coordinate

Neporo4naja [7]

Answer:

hope this helps you

4 0

3 years ago

Why are asymptotes important in rational function graphs

leonid [27]

Answer:

when sketching the curves of functions.

Step-by-step explanation:

There is a wide range of graph that contain asymptotes and that includes rational functions, hyperbolic functions, tangent curves, and more. Asymptotes are important guides when sketching the curves of functions. This is why it’s important that we know the properties, general forms, and graphs of each of these asymptotes.

6 0

2 years ago