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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Oceans one ocean at a time
Answer:
2/3
Step-by-step explanation:
Y varies directly as x
Y =kx
Y=6 when x = 72
First find the relationship between y and x.
i.e find the value of k
Substitute the value of x and y
6 = k *72
Make k the subject of the formula
K = 6/72
K= 1/12
:. The rlationship between x and y is
Y = 1/12x
When x is 8
Y = 1/12 * 8
Y = 8/12
Y = 2/3 and that is the answer
Hope it helped you
<span>See examples for the method to solving literal equations for a given variable: Solve A = bh for b. Since h is multiplied times b, you must divide both sides by h in order to isolate b. Since (c+d) is divided by 2, you must first multiply both sides of the equation by 2</span>
