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3 years ago

[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?

Mathematics

1 answer:

Nitella [24]3 years ago

6 0

Answer:

Step-by-step explanation:

Given the logarithmic equation

$\log_4x+\log_4(x-3)=\log_4(-7x+21)$

First, notice that

$x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x$

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

$\log_4x+\log_4(x-3)=\log_4x(x-3),$

then

$\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3$

Hence, $x=3$ and $x=-7$ are extraneous solutions

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Rudik [331]

20 is the answer to the question

4 0

3 years ago

Read 2 more answers

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

3/5 +9/10= Please answer<br>

Art [367]

Answer:

3/2 or 1.5

Step-by-step explanation:

Multiply 3/5 by 2 to make the denominator of both fractions equal.

2 x 3/5 = 6/10

Now that the denominators are equal, add the two fractions together

6/10 + 9/10 = 15/10 = 3/2 or 1.5

4 0

3 years ago

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Number of subsets of B={p,q,r}

oksian1 [2.3K]

Answer:

Step-by-step explanation:

B = {p , q , r}

Number of subsets = $2^{n}$

Her, n is the number of elements in the set.

Number of subsets = 2³ = 8

3 0

3 years ago

Which expression is m times m times m times m times m rewritten in exponential form? m Superscript 5 5 m 5 Superscript m m 5.

sukhopar [10]

The expression which is equal to the m times, m times, m times, m times, m rewritten in exponential form as,

$m^5$

<h3>What is the exponent or power?</h3>

The exponent or power of a number represent the multiplication of the that number to the power times.

Let suppose a number 2 has the power 2. Then it will be equal to,

$2^2=2\times2$

Similarly, 3 times of number 2 equal to the number 2 with exponent 3.

$2\times2\times2=2^3$

The expression is m times, m times, m times, m times, m. It can be written as,

$m\times m\times m\times m\times m\\$

The number m is total 5 time multiply by itself. Thus, the exponential form of the above equation is,

$m^5$

The expression which is equal to the m times, m times, m times, m times, m rewritten in exponential form as,

$m^5$

Learn more about the exponents power here;

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3 years ago