- #1
frozen7
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How to solve this?
ln ( ln ( ln ((e^x) +4)))=e
ln ( ln ( ln ((e^x) +4)))=e
frozen7 said:I do it in this way:
e^e = ln ( ln ( e^x +4))
e^e^e = ln (e^x +4)
e^e^e^e = e^x +4
x = 20
Is it correct? Or is there any others more easier way?
The purpose of this equation is to solve for the value of x that satisfies the given logarithmic expression.
To solve for x, we must first simplify the equation by using the properties of logarithms. We can use the fact that ln(e^x) = x and ln(ln(x)) = ln(x) to simplify the equation to ln(x+4) = e. Then, we can use the inverse property of logarithms to rewrite the equation as e^e = x+4. Finally, we can solve for x by subtracting 4 from both sides, giving us x = e^e - 4.
Yes, this equation can have multiple solutions. Since the exponential function is one-to-one, it is possible for e^x to equal different values, resulting in different solutions for x.
Yes, in order for the equation to have a solution, the value of e^x must be greater than -4, as the natural logarithm is undefined for negative numbers. Therefore, the domain for x is x > ln(-4).
No, this equation cannot be solved without using logarithms. The equation is in the form of ln(ln(ln(e^x + 4))) = e, and the only way to isolate x is by using the properties of logarithms.