The document discusses logarithms and includes examples of solving logarithmic equations, graphing logarithmic functions, and properties of logarithms and the natural logarithm function. Key points covered include:
- Logarithms are used to solve for exponents.
- Common properties include loga1=0, logaa=1, and logaax=x.
- Graphs of logarithmic functions f(x)=logax have a vertical asymptote at x=0 and an x-intercept at (1,0).
- Examples demonstrate evaluating logarithmic expressions, solving equations, and using a logarithmic formula to estimate the age of an archaeological sample.
Had to make this dumb powerpoint for my algebra II class and I put a lot of work into it for some reason... so yeah it's just been sitting on my laptop doing nothing and I thought why not upload this to help other people? So yeah, hope you guys find it useful...
Had to make this dumb powerpoint for my algebra II class and I put a lot of work into it for some reason... so yeah it's just been sitting on my laptop doing nothing and I thought why not upload this to help other people? So yeah, hope you guys find it useful...
The inverse of a function "undoes" the effect of the function. We look at the implications of that property in the derivative, as well as logarithmic functions, which are inverses of exponential functions.
The inverse of a function "undoes" the effect of the function. We look at the implications of that property in the derivative, as well as logarithmic functions, which are inverses of exponential functions.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Mel Anthony Pepito
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Lesson 16: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
We show the the derivative of the exponential function is itself! And the derivative of the natural logarithm function is the reciprocal function. We also show how logarithms can make complicated differentiation problems easier.
Lesson 16: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
We show the the derivative of the exponential function is itself! And the derivative of the natural logarithm function is the reciprocal function. We also show how logarithms can make complicated differentiation problems easier.