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3 years ago

If log a = x and log b = y, then log (ab2) equals

Mathematics

1 answer:

mylen [45]3 years ago

3 0

Answer:

The answer for log(ab²) is x + 2y.

Step-by-step explanation:

You have to apply Logarithm Law,

$log(a) + log(b) \: ⇒ \: log(a \times b)$

$log( {a}^{n} ) \: ⇒ \: n log(a)$

In this question, you have to seperate it out :

$log(a {b}^{2} ) = log(a) + log( {b}^{2} )$

$log( {b}^{2} ) = 2 log(b)$

$let \: log(a) = x$

$let log(b) = y$

$log(a {b}^{2} ) = log(a) + 2 log(b)$

$log(a {b}^{2} ) = x + 2y$

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What is the following product

Sloan [31]

Answer:

option D

60√3 - 21√6

...........

4 0

3 years ago

Peter Schmidt ordered sandwiches and salads for a luncheon meeting. The sandwiches cost three times as much as a salads. The tot

evablogger [386]

EXPLANATION

Let's see the facts:

$Sandwiches= 3*$Salads

Bill = $24.92

We can represent this in an equation:

Total Bill = Sandwiches + Salads

Let's call to Sandwiches "x" to Salads "y" and to Bill "B"

Then, the equation will be:

B = x+y = (3*y) + y

Applying distributive property:

24.92 = 3y + y

Adding similar terms:

24.92 = 4y

Dividing both sides by 4:

6.23 = y

Switching:

y=6.23

As we know, y variable represent the salads cost, so:

Answer is $6.23.

3 0

1 year ago

Which table has a constant of proportionality between y and x of 12?

Nikolay [14]

Answer & Step-by-step explanation:

To find if they have a constant of proportionality of 12, use the following:

$\frac{y}{x}=12$

Divide y by the x value (x,y), and if the remaining equation is true, then that table has a constant of proportionality of 12.*

:Done

*Make sure you check all the values in a table. Sometimes only the first values will have k=12, while the others don't.

**The constant of proportionality is represented by k.

3 0

3 years ago

Read 2 more answers

Find two unit vectos that are orthogonal to both [0,1,2] and [1,-2,3]

alekssr [168]

Answer:

Let the vectors be

a = [0, 1, 2] and

b = [1, -2, 3]

( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.

Let the cross product be another vector c.

To find the cross product (c) of a and b, we have

$\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]$

c = i(3 + 4) - j(0 - 2) + k(0 - 1)

c = 7i + 2j - k

c = [7, 2, -1]

( 2 ) Convert the orthogonal vector (c) to a unit vector using the formula:

c / | c |

Where | c | = √ (7)² + (2)² + (-1)² = 3√6

Therefore, the unit vector is

$\frac{[7,2,-1]}{3\sqrt{6} }$

[ $\frac{7}{3\sqrt{6} }$ , $\frac{2}{3\sqrt{6} }$ , $\frac{-1}{3\sqrt{6} }$ ]

The other unit vector which is also orthogonal to a and b is calculated by multiplying the first unit vector by -1. The result is as follows:

[ $\frac{-7}{3\sqrt{6} }$ , $\frac{-2}{3\sqrt{6} }$ , $\frac{1}{3\sqrt{6} }$ ]

In conclusion, the two unit vectors are;

[ $\frac{7}{3\sqrt{6} }$ , $\frac{2}{3\sqrt{6} }$ , $\frac{-1}{3\sqrt{6} }$ ]

and

[ $\frac{-7}{3\sqrt{6} }$ , $\frac{-2}{3\sqrt{6} }$ , $\frac{1}{3\sqrt{6} }$ ]

Hope this helps!

7 0

2 years ago

During a baseball game, a food stand sells popcorn for $2.50 and hotdogs for $3 each. If at the end of the game, the stand made

nasty-shy [4]

Let
x-------> bags of popcorn
y-------> bags of hotdogs

we know that
2.50x+3y=200-------> equation 1
x=2y--------> equation 2

substitute 2 in 1

2.50*[2y]+3y=200--------> 5y+3y=200------> 8y=200-----> y=200/8
y=25
x=2y-----> x=2*25-----> x=50

the answer is
50 bags of popcorn
25 bags of hotdogs

5 0

3 years ago