Answer:
Subtracting (negative) integers is the same as subtracting positive numbers.
By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> 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>
<em>Exponential</em> and <em>logarithmic</em> functions are <em>trascendental</em> functions, these are, functions that cannot be described <em>algebraically</em>. In addition, <em>logarithmic</em> functions are the <em>inverse</em> form of <em>exponential</em> 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
By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).
To learn more on logarithms: brainly.com/question/20785664
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The line equation in slope-intercept form is given by
where b is the y-intercept and m is the slope.
Then, we need to convert the given equation into the slope-intercept form. Then, by subtracting 10x to both sides, we have
and by dividing both sides by 2, we get
By comparing this result with the first equation, we can see that the slope is m= -5. So, the answer is: -5
The computation of the equation shows that the answers will be:
12. 340 units
13. 2(270) + (2 × x) = 690
14. x = 5
<h3>How to compute the equations?</h3>
12. The first equation that's given will be:
(13.50 × x) - (3.65 × x) = 3349
13.50x - 3.65x = 3349
9.85x = 3349
x = 3349/9.85
x = 340
The number to break even is 340 units
13. The equation that can be used to find the perimeter will be:
2(270) + (2 × x) = 690
540 + 2x = 690
2x = 690 - 540
2x = 150
x = 150/2 = 75
14. x + x + 2 + 8 = 20
2x + 10 = 20
2x = 20 - 10
2x = 10
x = 10/2
x = 5
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128 = 8d, because the product calls for multiplication to be performed.
