Why is the logarithmic conversion useful

We can never take the logarithm of a negative number. Also, we cannot take the logarithm of zero. Calculators may output a log of a negative number when in complex mode, but the log of a negative number is not a real number. First, identify the values of b , y , and x. To convert from exponential to logarithmic form, we follow the same steps in reverse.

We identify the base b , exponent x , and output y. Improve this page Learn More. Skip to main content. Module Exponential and Logarithmic Functions. The power of 0 dBm corresponds to a power of 1 mW. A 3 dBm increase corresponds to approximately double the power and a —3 dBm decrease corresponds to reducing the power by one-half. These two units are commonly used in fiber optic, microwave and radio networks, and control theory.

When dealing with receiving TV or radio antennas, it is more convenient to measure voltage instead of power. The voltage of 0 dBV corresponds to a voltage of 1 V. That is why the converter provides a field for entering a positive impedance value. We work hard to ensure that the results presented by TranslatorsCafe. However, we do not guarantee that our converters and calculators are free of errors.

Mobile View. Alexa Rank. Power Ratio in dB Power ratio relative to one watt or milliwatt. Amplitude Levels Ratio Voltage ratio relative to one volt or microvolt. Decibel to Power and Amplitude Ratio Converter The power and amplitude ratio must be a positive number.

Dry Volume and Cooking Measurements Pecks, bushels, hogsheads, cords — what are they? Absolute and Relative Reference Logarithmic Units A slide rule is an analog mechanical computer with several logarithmic scales.

John Napier Neper. Source: Wikipedia. William Oughtred. Digital sound level meter. Octave interval. The max. A C-message weighing filter mentioned in the definition of the dBrnC unit is employed for measuring signal-to-noise ratio. It was developed in North America for old-style telephones. The aperture of this manual fish-eye lens is set at 5. The Wi-Fi transmitter of this Linksys router can transmit The sensitivity of this Shure PG48 microphone is — Most professional headphones are capable of producing sound pressure exceeding 85 dB A , which is the maximum permissible sound pressure allowed to affect human hearing during a working day.

Calculators In this part of the TranslatorsCafe. W , watt? V , volt? Introduction History Definition Classification of Logarithmic Units Logarithmic Units for Amplitude and Power Examples of Relative Logarithmic Quantities and Units Examples of Absolute Logarithmic Units and Quantities in Decibels with Suffixes and Reference Values Introduction The sound power of a Saturn V rocket is ,, W or dB SWL A logarithmic scale is often used when there is a large range of quantities like sound pressure, earthquake strength, light intensity, various frequency-dependent values like musical intervals, in antenna engineering, electronics, acoustics, RF engineering.

History John Napier Neper. Source: Wikipedia Logarithms were invented because they allowed turning multiplication into addition, which can be made much faster than multiplication. Source: Wikipedia A key tool for the practical use of logarithms was the table of logarithms.

Definition The logarithm is the inverse operation to exponentiation. Digital sound level meter Relative logarithmic units , on the other hand, are used to express a physical value as a ratio or proportion of another physical value, for example in electronics where a decibel dB is commonly used to express the difference between two signals having arbitrary amplitudes.

Logarithmic Units for Amplitude and Power Power is proportional to amplitude squared. Examples of Relative Logarithmic Quantities and Units Common units dB decibel — a dimensionless logarithmic unit, which is used to express ratios of two arbitrary values of the same physical quantity.

For example, in electronics decibels are used to describe the gain of amplifiers or attenuation of a signal in cables. A decibel is defined as the ratio of one physical value to another value of the same physical quantity, which may be a reference value, multiplied by 10 for power values or by 20 for field amplitude values. B bel — a very rarely used dimensionless logarithmic unit, which is equal to 10 decibels. Np neper — a relative dimensionless logarithmic unit used to express ratios of two values, for example, the difference in voltage of two signals.

Nope, got it. Play next lesson. Try reviewing these fundamentals first What is a logarithm? Converting from logarithmic form to exponential form Evaluating logarithms without a calculator. That's the last lesson Go to next topic. Still don't get it? Review these basic concepts… What is a logarithm? Converting from logarithmic form to exponential form Evaluating logarithms without a calculator Nope, I got it. Play next lesson or Practice this topic. Play next lesson Practice this topic.

Start now and get better math marks! Lesson: 1. Intro Learn Practice. Logarithmic form Logarithms are inverses of exponential functions. Exponential form Although this lesson is on the logarithmic form, since logarithms are the inverses of exponential functions, we'll also have to quickly review the exponential form. Exponential form to logarithmic form So how do we switch from the exponential form that we're more familiar with, to the logarithmic form?

If I were working by hand, I would use the definition of logs to note that:. Why did I pick these particular x -values? Because anything smaller would have been too tiny to graph by hand, and anything larger would have led to a ridiculously wide graph. I picked the values that fit my needs. But, in this case, I'm supposed to be doing the graph with my graphing calculator. How can I do this? I don't have a "log-base-two" button. However, I can enter the given function into my calculator by using the change-of-base formula to convert the original function to something that's stated in terms of a base that my calculator can understand.

Flipping a coin, I choose the natural log:. I could have used the common log, too. In my graphing calculator, after adjusting the viewing window to show useful parts of the plane, the graph will look something like this:. By the way, you can check that the graph contains the expected "neat" points that is, the points I would have calculated by hand, as shown above to verify that the picture displays the correct graph:.