HSC Extension 1 and 2 Mathematics/Exponential and logarithmic functions

Index laws edit

Failed to parse (syntax error): {\displaystyle a^x × a^y = a^[(x+y)]} Failed to parse (syntax error): {\displaystyle a^x ÷ a^y = a^[(x-y)]}

Zero and negative indices edit

Rational indices edit

Exponential and logarithmic functions edit

Logarithms edit

Formula for converting one base to another edit

Derivative of exponential functions edit

 

Evaluation of e edit

Natural logarithms edit

Derivative of ekx, k a constant edit

 

 

Derivative of logex edit

 

 

Derivative of loge(ax), a > 0 edit

 

Derivative of loge(ax+b) edit

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikibooks.org/v1/":): {\displaystyle \frac{d}{dx}log_e(ax + b) = \frac{a}{ax + b}}