How Do You Solve Equations with Floor Functions and Logarithms?

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In summary, the Difficult Floor Function is a mathematical function that rounds a given number down to the nearest integer. It is denoted by the symbol ⌊x⌋ and is different from regular rounding as it always rounds down. It can be applied to any real number, including positive and negative numbers, fractions, and irrational numbers, as well as complex numbers. The purpose of the Difficult Floor Function is to aid in various mathematical and scientific applications. Special cases include when the input is already an integer, in which case the function returns the input, and when the input is negative, in which case it rounds down to the nearest integer less than the input.
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inqusoc
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hi I'm new here. For a couple of days i am struggling to methodically solve an equation involving the integer part of a fraction but nothing yet. The equation is;
upload_2015-8-15_18-12-46.png

I found that the apparent solution is 53 as x HAS to be integer. Yet, I cannot mathematically prove how to compute x to be equal to 53. Any opinion is welcome, thanks!
 

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There is no way to solve the equation analytically with x and ln(x) like that. Numerical approaches are the best option, for small integer x this just means trial and error.

52 to 56 all work for x.
 

What is the Difficult Floor Function?

The Difficult Floor Function, also known as the floor function or greatest integer function, is a mathematical function that rounds a given number down to the nearest integer. It is denoted by the symbol ⌊x⌋.

How is the Difficult Floor Function different from regular rounding?

The Difficult Floor Function always rounds down to the nearest integer, while regular rounding rounds to the nearest whole number. For example, ⌊3.5⌋ = 3, while rounding 3.5 would result in 4.

What types of numbers can the Difficult Floor Function be applied to?

The Difficult Floor Function can be applied to any real number, including positive and negative numbers, fractions, and irrational numbers. It can also be applied to complex numbers.

What is the purpose of the Difficult Floor Function?

The Difficult Floor Function is useful in many mathematical and scientific applications, such as calculating the number of items needed for a project, determining the number of people in a group, or finding the largest integer less than or equal to a given number.

Are there any special cases or exceptions for using the Difficult Floor Function?

One special case is when the input is already an integer, in which case the Difficult Floor Function will simply return the input as the output. Another exception is when the input is a negative number, in which case the Difficult Floor Function will round down to the nearest integer that is less than the input.

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