Math Tutoring on Evaluating Logarithmic Expressions
To evaluate Logarithmic Expressions we need to know the properties of logarithmic functions in math tutoring. Following are the properties of logarithms:
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 of 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.
logₐ x = ( logᵣ x ) / ( logᵣ a ) .
There is no need that either base 10 or base e be used.
logₐ x = ( log x ) / ( log a ) = ( ln x ) / ( ln a ).
So, during math tutoring when evaluating logarithms all that we are really asking is what exponent did we put onto the base to get the number in the logarithm?
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1. What is the parent function of a logarithmic equation?
2. How do you graph a natural log?
3. What is the base formula for converting between different bases?
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