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konstantin123 [22]
2 years ago
9

Solve: 2 In 3 = In(x-4)

Mathematics
1 answer:
Alona [7]2 years ago
5 0

\bf \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf 2\ln(3)=\ln(x-4)\implies \ln(3^2)=\ln(x-4)\implies \ln(9)=\ln(x-4) \\\\\\ \log_e(9)=\log_e(x-4)\implies e^{\log_e(9)}=e^{\log_e(x-4)}\implies 9=x-4\implies \boxed{13=x}

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If the first step in the solution of the equation -9+x=5x-7 is "subtract x", then what should the next step be
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3 years ago
Maya runs a farm stand that sells raspberries and blueberries. Each pound of raspberries sells for $1 and each pound of blueberr
aniked [119]

30 pounds of raspberries and 50 pounds of blueberries are sold

<em><u>Solution:</u></em>

Let "a" be the pounds of raspberries sold

Let "b" be the pounds of blueberries sold

Cost per pound of raspberry = $ 1

Cost per pound of blue berry = $ 3.25

<em><u>Maya made $192.50 from selling a total of 80 pounds of raspberries and blueberries</u></em>

Therefore,

a + b = 80

a = 80 - b ------- eqn 1

<em><u>Maya made $192.50. Therefore, frame a equation as:</u></em>

pounds of raspberries sold x Cost per pound of raspberry + pounds of blueberries sold x Cost per pound of blue berry = 192.50

a \times 1 + b \times 3.25 = 192.50

a + 3.25b = 192.50 ------ eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Substitute eqn 1 in eqn 2</u></em>

80 - b + 3.25b = 192.50

2.25b = 192.50 - 80

2.25b = 112.5

Divide both sides by 2.25

b = 50

<em><u>Substitute b = 50 in eqn 1</u></em>

a = 80 - 50

a = 30

Thus 30 pounds of raspberries and 50 pounds of blueberries are sold

3 0
3 years ago
Elizabeth is making lemonade. She uses a box of mix to make of a gallon. How much mix will she need to make one gallon?
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Whats the answer for 5x+14=k
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The following table shows the length and width of a rectangle: Length Width Rectangle A 3x 2 2x − 1 Which expression is the resu
Stolb23 [73]

The perimeter of a rectangle is 10x + 2 which is a polynomial function. Option C is the correct answer.

<h3>What is a perimeter?</h3>

A perimeter is a closed path that outlines either a two-dimensional shape or a one-dimensional length.

Given that the length is 3x+2 and the width is 2x-1. The perimeter of a rectangle is given below.

P = 2 (L + W)

P = 2 ( 3x+2 + 2x-1)

P = 2 ( 5x +1)

P =10x +2

A polynomial function is a function that involves only positive integer exponents of a variable in an equation.

Hence we can conclude that the perimeter of a rectangle is 10x + 2 which is a polynomial function. Option C is the correct answer.

To know more about the perimeter, follow the link given below.

brainly.com/question/6465134.

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