5.5 Properties and Applications of Logarithms
To expand a logarithm consists of using the above properties to rewrite the logarithm as a
combination of simpler logarithms.
To condense a logarithm consists of using the above properties to bring together a bunch of
logarithms into a single logarithm.
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Expand the logarithms into many logarithms using these properties.
1)
2)
Condense the expressions involving logarithms into a logarithm using the properties above.
1)
2)
2
Change of base formula:
Therefore:
Example:
In fact, changing the base is often the often the only way to calculate
a logarithm with a calculator, which usually only has log and ln.
Use this formula and your calculator to find the following logarithms to three decimal places:
1)
2)
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pH of a solution is defined as:
negative log base 10 of the
concentration of the hydronium ions
Acidic: pH less than 7
Basic: pH more than 7
If a sample of lemonade has a hydronium ion concentration of 7.22 x 10­3 moles per liter then find the pH:
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You Try:
1) Expand:
.
2) Decibel formula:
I is the intensity of the sound
I0 is the intensity of a justdiscernable sound.
Assume I0=10­12 watts/meter2. What is the decibel level of an airliner's engines 45 meters away, if the intensity 45 meters away is 50 watts/meter2.
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