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:
0.002 pounds
Step-by-step explanation:
1lb / 500 = 0.002 pounds
Answer:
B.) 3
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
x - y = -1
3x + 5y = 21
<u>Step 2: Rewrite Systems</u>
x - y = -1
- Add <em>y</em> to both sides: x = y - 1
<u>Step 3: Redefine Systems</u>
x = y - 1
3x + 5y = 21
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 3(y - 1) + 5y = 21
- Distribute 3: 3y - 3 + 5y = 21
- Combine like terms: 8y - 3 = 21
- Add 3 to both sides: 8y = 24
- Divide 8 on both sides: y = 3
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