Solution - Adding and subtracting logarithms

\log (14)

log(14)

Decimal form:

1.146

1.146

See steps

Step-by-step explanation

1. Add/Subtract the logarithms

$\log (6) - \log (3) + \log (7)$

To subtract the logarithms, use the rule: $l o g_{a} (x) - l o g_{a} (y) = l o g_{a} (x / y)$ :

$l o g (6 / 3) + l o g (7)$

Reduce the fraction(s):

$\log (2) + \log (7)$

To add the logarithms, use the rule: $\log_{a} (x) + \log_{a} (y) = \log_{a} (x y)$ :

$\log (2 \cdot 7)$

Multiply the arguments:

$\log (14)$

2. Decimal form

$\log (14) = 1.146$

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Why learn this

Understanding logarithmic scales is vitally important to anyone who works with data on a regular basis. The Richter Scale, which measures the strength of earthquakes, is a classic example of a logarithmic scale, as are decibels (a measurement of sound intensity), lumens (a measurement of light intensity), and pH (a measurement of acidity or basicity of almost anything). One of their most important features is their relationship to exponential functions. Logarithms can be used to solve exponential equations and, therefore, explain certain phenomena like the spread of a virus or growth of a certain population over time.

As you might have guessed from these examples, logarithms tend to be more useful in ways that we cannot see but are essential for making sense of our world. For this reason, they are a crucial part of many professions, especially those in math and science.

Terms and topics

Logarithms