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Ln(x+1)-Ln(x+4)=4
Using the fact that
-log(b)=log(1/b) and log(a)+log(c)=log(a*c),
log(a)-log(b)=log(a)+log(1/b)=log(a/b). ...[#1]
Thus, if we let a=x+1, b=x+4, using the relationship in [#1]
log(x+1)-log(x+4)=4 is equivalent to
log[(x+1)/(x+4)]=4.....taking the anti-log,
(x+1)/(x+4)=exp(4)
x+1=(e^4)*x+4*(e^4)
1-4*(e^4)=[(e^4)-1]x
x=[1-4*(e^4)]/[(e^4)-1]
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Josh
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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.
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