Math Tutoring on Using the Properties of Logarithms
Following are the properties of logarithms:
Product Property: The log of a product equals the sum of the logs.
1. logₐ (uv) = logₐ u + logₐ v or ln (uv) = ln u + ln v
Quotient Property: The log of a quotient equals the difference of the logs.
2. logₐ (u / v) = logₐ u - logₐ v or ln (u / v) = ln u - ln v
Power Property: The log of a power equals the product of power and the log
3. logₐ un = n logₐ u or ln un = n ln u
Also few more properties on logarithms:
1. logₐ1 = 0 since a° = 1
2. logₐa = 1 since a¹ = 1
3. logₐaᵐ = m since aᵐ = a
There is a change of base formula for converting between different bases.
There is no need that either base 10 or base e be used.
logₐ x = ( log x ) / ( log a ) = ( ln x ) / ( ln a ).
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1. What is the base formula for converting between different bases?
2. What are the different properties of the logarithm?
3. Explain power property of logarithms.
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