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Use the following steps to prove that log b(xy)- log bx+ log by. a. Letx-bp and y= bq. Solve these expressions for p and q, respectively
b. Use the property b*b b to express xy in terms of b, p, and q
c. Compute log b(xy) and simplify

Answers

Answer 1

Answer:

Answer with Step-by-step explanation:

a. $x=b^p$

$y=b^q$

Taking both sides log

$log x=plog b$

Using identity: $logx^y=ylogx$

$p=(logx)/(log b)=log_b x$

Using identity: $log_x y=(log y)/(log x)$

$log y=qlog b$

$q=(log y)/(log b)=log_b y$

b. $xy=b^pb^q$

We know that

$x^a\cdot x^b=x^(a+b)$

Using identity

$xy=b^(p+q)$

c. $log_b(xy)=log_b(b^(p+q))$

$log_b(xy)=(p+q)log_b b$

Substitute the values then we get

$log_b(xy)=(log_b x+log_b y)$

By using $log_b b=1$

Hence, $log_b(xy)=log_b x+log_b y$

Answer 2

Answer:

Final answer:

To prove the property log b(xy) = log bx + log by, we let x = $b^p$ and y = $b^q$ , express xy in terms of the base b and the exponents p and q, and then use the properties of logarithms to show the equality.

Explanation:

The student is asking to prove the logarithmic property − log b(xy) = log bx + log by. Here's a step-by-step explanation:

Let x = bp and y = bq. To solve for p and q, take the logarithm base b of both sides. Thus, p = logbx and q = logby.

Using the property of exponents, xy = bp*bq = bp+q.

Now compute logb(xy). According to the logarithmic property, logb(bp+q) = p + q. Since p = logbx and q = logby, then logb(xy) = logbx + logby.

Therefore, we have proven the given logarithmic property using the steps provided in the question.

Learn more about Logarithmic Properties here:

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suppose that you made four measurement of a speed of a rocket: 12.7 km/s, 13.4 km/s, 12.6 km, and 13.3 km/s. compute: the mean, the standard deviations, and the standard deviation of the mean

Answers

Answer:

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second

Step-by-step explanation:

We are given the following data set of rocket speed in kilometer per second in the question:

12.7, 13.4, 12.6, 13.3

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle(52)/(4) = 13$

Deviations from mean = -0.3, 0.4, -0.4, 0.3

Sum of squares of differences =

0.09 + 0.16 + 0.16 + 0.09 = 0.5

$S.D = \sqrt{(0.5)/(3)} = 0.4082$

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second

What is the answer to a10/a3 ?

Answers

Answer:

a^7

Step-by-step explanation:

$(a^(10))/(a^3)\n\n\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\n(a^(10))/(a^3)=a^(10-3)\n\n=a^7$

Find the slope of the line that passes through the pair of points.

(2,2) AND (-2,-2)

Answers

Answer:

the slope is 1

Step-by-step explanation:

the formula is (y1-y2)/(x1-x2)

this comes out to 4/4 which equals 1

Answer:

Step-by-step explanation:

by using formula

$(y_2-y_1)/(x_2-x_1)=(-2-2)/(-2-2)=(-4)/(-4)=1$

3x=2x+50 solve for x

Answers

The value of x for the given equation is given as x = 50.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is as below,

3x = 2x + 50

It can be solved as follows,

3x = 2x + 50

=> 3x - 2x = 50

=> x = 50

Hence, the solution of the given linear equation is x = 50.

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this is the answer to your question x=50

Step-by-step explanation:

3x-2x=50

1x=50

"write a program that takes as input an arithmetic expression. the program outputs whether the expression contains matching grouping symbols. for example, the arithmetic expressions {25 + (3 – 6) * 8} and 7 + 8 * 2 contains matching grouping symbols. however, the expression 5+{(13+7)/8-2*9 does not contain matching grouping symbols."

Answers

theprogram outputs whether the expression contains matching groupingsymbols. for example, the arithmetic expressions {25 + (3 – 6) * 8} and 7+ 8 * 2 contains matching grouping symbols. however, the expression5+{(13+7)/8-2*9 does not contain matching grouping symbols.

Describe how the graph of y | x| -4 is like the graph of y= |x| and how it is different.

Answers

The graph y=|x|-4 is obtained from the graph y=|x| dy moving down 4 units the graph y=|x| along the y-axis (see, if x=0, then for y=|x|, y=0 and for y=|x|-4, y=-4).

These two graphs have the same form.

Answer:

The graph of y=|x|-4 is the same as y=|x|.

Step-by-step explanation:

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