All categories

2 years ago

choose the single logarithm expression that is equivalent to the one shown 1 / 3 log 3x + 2 / 3 log 3x

Mathematics

1 answer:

alexgriva [62]2 years ago

6 0

Answer:

$\log (3x)$

Step-by-step explanation:

The given logarithmic expression is:

$\frac{1}{3}\log(3x)+ \frac{2}{3}\log(3x)$

This is the same as:

$\frac{1}{3}\log(3x)+ \frac{1}{3}\log(3x)^2$

$\frac{1}{3}(\log(3x)+ \log(3x)^2)$

We now apply the product rule to get:

$\frac{1}{3}\log(3x)\times (3x)^2$

$\frac{1}{3}\log (3x)^3$

We now apply the power rule to get;

$\frac{3}{3}\log (3x)=\log (3x)$

You might be interested in

Module 04.03 Exponential Functions and Models: Essential Questions:

azamat

1. Exponents are the repeated multiplication of a number. It is represented by the formula of a^n where a is the number to be repeated and n is the number of times the number is being multiplies by itself. Also include the sign of the number, no matter how it is multiplied, it is still important. For instance you have 4(4), you have 4 as the repeated number. You can see that it is multiplied by itself by two times. So you have (-4)^2.

2. Graphs and tables are the key features in finding a model between two quantities. If he data values, after plotting it into a graph, produces a straight line, then you will have a direct relationship between the two and sometimes you can get an equation of the line. Sometimes it will give you a curved line. That is why it is important to graph the values of the table to better understand the relationship between two variables.

4 0

3 years ago

Todd has twice as many songs in his playlist as Vlad. Becca has three times as many songs in her playlist as Todd. If all three

nikitadnepr [17]

Answer:

Todd has 540540 songs in his playlist.

Vlad has 270270 songs in his playlist.

Becca has 162162 songs in her playlist.

Step-by-step explanation:

# of songs Todd has = T

# of songs Vlad has = V

# of songs Becca has = B

1) Todd has twice as many songs in his playlist as Vlad:

T=2V

2) Becca has three times as many songs in her playlist as Todd:

B=3T

3) All three people have a total of 243243 songs in their playlists:

T+V+B=243243

Because T=2V then you can substitute T as 2V in the second equation:

B=3(2V)

B=6V

Now in the final equation, you can substitute everything for V:

2V+V+6V=243243

9V=243243

V=27027

Now substitute for T:

T+1/2T+3T=243243

9/2T=243243

T=54054

Now substitute for B:

1/3B+1/6B+B=243243

3/2B=243243

B=162162

Check answers:

27027+54054+162162=243243

243243=243243

3 0

2 years ago

A spinner is split into 4 equal parts labeled 1, 2, 3, and 4.

ivolga24 [154]

Answer:

50%

Step-by-step explanation:

If there are 4 parts to the spinner, 4 is the whole. Since there are 2 even numbers (2&4), the fraction would be $\frac{2}{4}$ , which is simplified to $\frac{1}{2}$ . And because $\frac{1}{2}$ could also turn into $\frac{50}{100}$ , the percentage is 50%.