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1 year ago

7^x=3^[x+4] solve x using logarithmic

1 answer:

4 0

By taking advantage of the definition of exponential and logarithmic function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

<h3>How to solve an exponential equation by logarithms</h3>

Exponential and logarithmic functions are trascendental functions, these are, functions that cannot be described algebraically. In addition, logarithmic functions are the inverse form of exponential functions. In this question we take advantage of this fact to solve a given expression:

7ˣ = 3ˣ⁺⁴ Given
㏒ 7ˣ = ㏒ 3ˣ⁺⁴ Definition of logarithm
x · ㏒ 7 = (x + 4) · ㏒ 3 ㏒ aᵇ = b · ㏒ a
x · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3 Distributive property
x · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3 Existence of additive inverse/Modulative and associative properties
x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3) Existence of multiplicative inverse/Modulative property/Result

To learn more on logarithms: brainly.com/question/20785664

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Solve. Chanasia has 6.25 gallons of paint. She wants to use 2/5 of the paint to paint her living room. How many gallons of paint

deff fn [24]

Answer: 2.5 gallons

Step-by-step explanation:

Given that:

Gallons of paint had = 6.25 gallons

Amount needed to paint room = 2/5 of the paint

Gallons of paint needed :

2/5 of 6.25

(2 * 6.25) / 5 gallons

= 12.5 / 5

= 2.5 gallons

3 0

3 years ago

NO LINKS!!!!

mixer [17]

Hope this help!!!

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7 0

2 years ago

PLEASE HELP!!!! I need to solve for a, b, and c

nirvana33 [79]

Answer:

25000 seats in section A
14100 seats in sectin B
10900 seats in section C

Step-by-step explanation:

The problem statement tells you half the total number of seats are in section A, so you already know that there are 25000 A seats. The revenue from those seats is

... 25000×$25 = $625,000

so the revenue from B and C seats must total

... $1,070,500 - 625,000 = $445,500

If all 25000 of the B/C seats were C seats, the revenue would be

... 25000×$15 = $375,000

The actual revenue from those seats is $445,500 -375,000 = $70,500 more than that. We know each B seat generates $5 more revenue, so there must be ...

... $70,500/$5 = 14,100 . . . . B seats

Then the balance of the 25000 B and C seats are C seats:

... 25,000 - 14,100 = 10,900 . . . . C seats

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Alternate Solution Method

The new Brainly answer format requires the answer be supplied before the working. In order to find the answer quickly so that I can fill in that section, I used a matrix method for solving the problem. The problem equations can be written ...

a + b + c = 50000
a - b - c = 0
25a + 20b + 15c = 1070500

so the augmented matrix is ...

$\left[\begin{array}{cccc}1&1&1&50000\\1&-1&-1&0\\25&20&15&1070500\end{array}\right]$

A graphing calculator can be used to find the solution to this, generally using a function that produces the reduced row-echelon form. The attachment shows the solution using a TI-84 calculator.

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Comment on the Working

Since the number of A seats is equal to the total of B and C seats, the number of A seats must be half the total number of stadium seats. Having figured that out, the problem is reduced to one of finding the mix of B and C seats that will produce the remaining revenue.

As with many mixture problems, it is convenient to look at differences. Start with the assumption that all of the desired revenue comes from the least contributor. Here, that is C seats. Then figure the difference that using a B seat makes ($20 -15 = $5) and the difference of the actual revenue and the amount that you got by assuming all C seats: 445,500 -375,000 = 70,500. Since replacing a C seat by a B seat adds $5 to the revenue, it is easy to figure the number of such replacements required in order to raise the revenue by $70,500.

If you write the equation for B seats, you find the solution to the equation mirrors this verbal description:

... 20b + 15(25000-b) = 445,500

... 5b = 445,500 - 375000 . . . . simplify, subtract 375000

... b = 70500/5 = 14100