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2 years ago

What is the power property of logarithms?

Mathematics

1 answer:

Ulleksa [173]2 years ago

7 0

Log(a)^b=b*log(a)
is the power property of logarithms

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He stem and leaf plot shows the number of calories in one serving for 12 different snack foods.

masha68 [24]

Answer:

Step-by-step explanation:

my sis keep telling me the answers (︶^︶) ◑︿◐

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2 years ago

Read 2 more answers

Please select the best answer from the choices provided

Ira Lisetskai [31]

<u>Answer:</u>

The correct answer option is c. $\frac{1}{9a^2}$ .

<u>Step-by-step explanation:</u>

We are given an expression $(27a^{-3})^{-\frac{2}{3} }$ and we are supposed to simplify it.

We can also write $(27a^{-3})^{-\frac{2}{3} }$ as $(\frac{3^3}{a^3} )^{-\frac{2}{3} }$ .

We know the power rule (a^m)^n=a^{mn} which means that to raise a power to a power you need to multiply the exponents.

So multiplying the exponents to get:

$\frac{3^{(3.-\frac{2}{3})} }{a^{(3.\frac{2}{3})} }\\\\\frac{3^{-2}}{a^2}\\ \\\frac{1}{3^2a^2} \\\\\frac{1}{9a^2}$

Therefore, the correct answer option is c. $\frac{1}{9a^2}$ .

4 0

3 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

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8 months ago

Which number is rational?

salantis [7]

The last one is rational because it is a terminating decimal.

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3 years ago

Write words to match the expressions

velikii [3]

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2 years ago