blog

commit

83c571398b8494fb482bc6825c360a0350bd9173

parent

70299e8e7f58e0cee8b59fbd65fcc1ae43543504

Author

Tobias Bengfort <tobias.bengfort@posteo.de>

Date

2025-07-11 12:18

use block math

Diffstat

2 files changed, 4 insertions, 4 deletions

diff --git a/_content/posts/2025-05-16-tax-curves/index.md b/_content/posts/2025-05-16-tax-curves/index.md

@@ -29,7 +29,7 @@ lowering taxes.
   29    29 
   30    30 The simplest model is a flat tax rate with basic income:
   31    31 
   32    -1 $f(x) = ax+b$
   -1    32 $$f(x) = ax+b$$
   33    33 
   34    34 ![](linear.png)
   35    35 
@@ -49,7 +49,7 @@ your income, the higher your marginal tax rate. Or: your income after tax still
   49    49 grows, but it grows slower. The classic mathematical function that grows to
   50    50 infinity but slows down while doing so is the logarithm:
   51    51 
   52    -1 $f(x) = a \ln(\frac{x}{a} + 1) + b$
   -1    52 $$f(x) = a \ln(\frac{x}{a} + 1) + b$$
   53    53 
   54    54 ![](log.png)
   55    55 
@@ -67,7 +67,7 @@ money than everyone else.
   67    67 Another type of functions that go up to infinity but slow down on the way are
   68    68 power functions like this one:
   69    69 
   70    -1 $f(x) = (\frac{x}{ab} + 1)^a b$
   -1    70 $$f(x) = (\frac{x}{ab} + 1)^a b$$
   71    71 
   72    72 ![](pow.png)
   73    73 

diff --git a/_content/posts/2025-06-23-loudness/index.md b/_content/posts/2025-06-23-loudness/index.md

@@ -233,7 +233,7 @@ Loudness is typically measured as logarithm of power, which in turn is
  233   233 calculated as the integral over the squared audio signal. In the case of ITU-R
  234   234 BS.1770-S:
  235   235 
  236    -1 $Loudness(y) = 10 \log_10\left(\int_{t=0}^T y(t)^2 dt\right) - 0.691$
   -1   236 $$Loudness(y) = 10 \log_10\left(\int_{t=0}^T y(t)^2 dt\right) - 0.691$$
  237   237 
  238   238 The unit for loudness is LKFS (Loudness, K-weighted, relative to full scale).
  239   239 EBU uses the same unit, but calls it LUFS (Loudness units relative to full