Question

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

Answer 1

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).

How to solve an exponential equation by logarithms

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:

1. 7ˣ = 3ˣ⁺⁴     Given
2. ㏒ 7ˣ = ㏒ 3ˣ⁺⁴      Definition of logarithm
3. x · ㏒ 7 = (x + 4) · ㏒ 3     ㏒ aᵇ = b · ㏒ a
4. x · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3     Distributive property
5. x · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3      Existence of additive inverse/Modulative and associative properties
6. x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3)     Existence of multiplicative inverse/Modulative property/Result

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).

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

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