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Proof of the change of base formula for logarithms.
Math: Pre-K - 8th grade; Pre-K through grade 2 (Khan Kids) Early math review; 2nd grade; 3rd grade; 4th grade; 5th grade; 6th grade; 7th grade; 8th grade; See Pre-K - 8th Math
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Unit 1 Polynomial arithmetic. Unit 2 Complex numbers. Unit 3 Polynomial factorization. Unit 4 Polynomial division. Unit 5 Polynomial graphs. Unit 6 Rational exponents and radicals. Unit 7 Exponential models. Unit 8 Logarithms. Unit 9 Transformations of functions.
Learn how to rewrite any logarithm using logarithms with a different base. This is very useful for finding logarithms in the calculator!
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So we have the log of x plus the log of 3 is equal to 2 times the log of 4 minus the log of 2, or the logarithm of 2. And this is a reminder. Whenever you see a logarithm written without a base, the implicit base is 10.
The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits.
Sal rewrites logarithmic expressions like 1/(logₐ4) or logₐ(16)*log₂(a) using the change of base rule.
Sal approximates log₅(100) by rewriting it as log(100)/log(5) using the change of base rule, then evaluates with a calculator.