Solving a logarithmic equation $\log_2 (2^x-1)+x=\log_4 (144)$
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Solving a logarithmic equation $\log_2 (2^x-1)+x=\log_4 (144)$

I need to solve this: $$\log_2 (2^x-1)+x=\log_4 (144)$$ I can work out that $x=\log_2 (2^x)$ and $\log_4 (144)=log_2(12)$ but I'm stuck after that.

Published: Aug 17, 2026

Trichotomy implies totality of partial order
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Trichotomy implies totality of partial order

Theorem: A partially ordered set is totally ordered if it obeys the law of trichotomy. Things I know: A relation on some set $A$ is said to be a partially...

Published: Aug 17, 2026

Prove the randomness of elements in list
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Prove the randomness of elements in list

I wrote a function that generates random numbers (but not with libraries) I could use numpy or statistic library in python, But generate them from scratch...

Published: Aug 17, 2026

Definition of an Ordered Field
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Definition of an Ordered Field

A text I'm looking at has the following definition of an ordered field: DEFINITION A field ($F$, $+$, $\cdot$) is ordered iff there is a relation $\l...

Published: Aug 17, 2026

Smallest possible dimensions of a piece of paper after one fold.
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Smallest possible dimensions of a piece of paper after one fold.

So I've been thinking, can someone explain mathematically if I started with a square of paper dimensions 1x1, what the smallest single side dimension...

Published: Aug 17, 2026

How to express a sum of two series in terms of known sums? [closed]
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How to express a sum of two series in terms of known sums? [closed]

If i have $\sum_{n=1}^\infty a_n=A$ and $\sum_{n=1}^\infty b_n=B$, can i write $\sum_{n=1}^\infty a_n\cdot b_n$ in function of $A$ and $B$ ?

Published: Aug 17, 2026

Multiplying radicals by variables
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Multiplying radicals by variables

Let's say I am to multiply $3x^2$ by ${\sqrt 8}$. Which answer is true and why? $3 {\sqrt 8x^2}$ or $3x^2 {\sqrt 8}$

Published: Aug 17, 2026

You roll a 6 sided die what is p(6 or even)? Simplified your answer and write it as a fraction or whole number. We NEED answers for IXL! [closed]
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You roll a 6 sided die what is p(6 or even)? Simplified your answer and write it as a fraction or whole number. We NEED answers for IXL! [closed]

You roll a 6 sided die. What is p(6 or even)? Simplified your answer and write it as a fraction or whole number. You roll a 6-sided die. I am working on t...

Published: Aug 17, 2026

What is the difference between continuous derivative and derivative?
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What is the difference between continuous derivative and derivative?

What is the difference between continuous derivative and derivative? According to my teachers solution to the assignment,it seems there exits difference b...

Published: Aug 17, 2026

Division of a Convex Shape results in a Convex Shape
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Division of a Convex Shape results in a Convex Shape

Let $P$ be almost a convex polygon in the plane. By almost, we mean that some edges could be arcs and not just line segments, as long as $P$ remains conve...

Published: Aug 17, 2026

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