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Related Concept Videos

Laws of Logarithms II01:28

Laws of Logarithms II

Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
Laws of Logarithms I01:30

Laws of Logarithms I

Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
Introduction to Logarithmic Functions01:14

Introduction to Logarithmic Functions

Logarithmic functions are the inverses of exponential functions and are used to solve for exponents. The general form is y = logₐ(x), where a > 0 and a ≠ 1. This function returns the power to which the base a must be raised to obtain x. The logarithmic function is only defined for x > 0, and its range includes all real numbers.Graphically, logarithmic and exponential functions are reflections of each other across the line y = x. The graph of y = logₐ(x) passes through (1, 0) and has a...
Generation Time01:22

Generation Time

Bacterial generation time, the period required for a bacterial population to double during its exponential growth phase, serves as a critical measure of microbial growth dynamics under optimal conditions. This parameter varies significantly across bacterial species and can be influenced by factors such as temperature, pH, and the availability of nutrients. For example, Escherichia coli can achieve a generation time of approximately 20 minutes, while Mycobacterium tuberculosis exhibits a much...
Applications of Logarithms01:28

Applications of Logarithms

Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...

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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

Simple logarithmic time base generator.

E F Denby1, L J Wills

  • 1Division of Textile Physics, Commonwealth Scientific and Industrial Research Organization, 338 Blaxland Road, Ryde, Sydney, N.S.W. 2112, Australia.

The Review of Scientific Instruments
|February 1, 1978
PubMed
Summary
This summary is machine-generated.

A low-cost digital device using three CMOS chips generates a log-time function across seven decades. Modifications can enhance its range and accuracy for broader applications.

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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Area of Science:

  • Electronics
  • Signal Processing
  • Instrumentation

Background:

  • Accurate generation of logarithmic time functions is crucial for various scientific and engineering applications.
  • Existing methods for log-time generation can be complex or costly.

Purpose of the Study:

  • To describe a novel, inexpensive digital device for generating log-time functions.
  • To detail simple modifications for improving the device's performance.

Main Methods:

  • The device utilizes three cost-effective CMOS chips.
  • It is designed to produce a log-time output over a wide dynamic range.

Main Results:

  • The device successfully generates the log-time function over seven decades of time.
  • Modifications were identified to increase both the operational range and accuracy.

Conclusions:

  • A simple, affordable digital device can effectively generate log-time functions.
  • The described modifications offer a pathway for enhanced performance and versatility.