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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Answer:
She will receive $24,000 after paying taxes
Step-by-step explanation:
This question can be solved using a rule of three.
20% of her money has to go to the state for taxes. So she will receive 100-20 = 80%. $30000 is 100% = 1. How much is 80% = 0.8?
$30000 - 1
$x - 0.8
x = 30000*0.8
x = 24000
She will receive $24,000 after paying taxes
Remark
This is quite a nice little problem. It takes a minute or three to figure out the answer, and when you do, you will be certain that you have been tricked. It is a little like the egg of Columbus.
Solution
The Base of Triangle ABN is AB
The Base of Triangle CDM is CD
The height of both given triangles is h. That is the distance between the two parallel lines.
Area ABN = 1/2*AB * h = 23 cm^2
Area CDM = 1/2*CD * h = 18 cm^2
Now the Area of the trapezoid is
Area_Trapezoid = 1/2 * h (AB + CD) Using the distributive property Remove the brackets.
Area_Trapezoid = 1/2*AB*h + 1/2*CD*h Did you notice something? Those terms are just the area of the triangles (written above.)
Area Trapezoid = 23 + 18 = 41 cm^2 <<<< Answer
4/5 to get a rational number bc it would be 5. hope it helps.
5 over the power if two divide 6 from what you get and that is your answer
