Answer :
Answer:
x = 0.5240
Step-by-step explanation:
(Natural) Logarithm Properties
Quotient Property
[tex]\rm log_b(a)-log_b(c)=log_b(\dfrac{a}{c} )[/tex],
where b is the base and a and c are distinct arguments (the number that b raised to a certain power equals to).
Exponential Property (Natural)
[tex]\rm e^l^n^(^x^)=x[/tex],
where e is Euler's Number or the natural constant and ln is the natural logarithm with base of e.
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Solving the Problem
The left hand side follows the quotient property so it can be rewritten into one big natural log.
[tex]\rm ln(\dfrac{x+10}{x} )=3[/tex]
We can't solve for x until the x terms are isolated so, we can use the exponential property to remove the natural log.
[tex]\rm e^l^n^(^\frac{x+10}{x} ^)=e^3[/tex]
[tex]\rm \dfrac{x+10}{x} =e^3[/tex]
All there's left is to solve for x using algebra!
[tex]\rm x+10=xe^3[/tex]
[tex]\rm 10=xe^3-x[/tex]
[tex]\rm 10=x(e^3-1)[/tex]
[tex]\rm \dfrac{10}{e^3-1} =x[/tex]
[tex]\rm 0.5240=x[/tex]
