











A general rule for exponents 

x^{a/b} = ^{b}vx^{a} = (^{b}vx)^{a} 


the base10 system the natural system 

base10 system for exponents 


natural system for exponents 


the logarithm of a number is equal to… 


the natural logarithm of a number is equal to… 


how to do log for the base10 rule 

log x = log_{10}(10^{b}) = b 

how to do log for the natural system 

ln x = log_{e} x = log_{e}(e^{a}) = a 

what happens to exponents when numbers are multiplied 

10^{b} · 10^{c} = 10^{b+c}e^{b} · e^{c} = e^{b+c} 

what happens to exponents when numbers go thru division 

10^{b} / 10^{c} = 10^{bc}e^{b} / e^{c} = e^{bc} 

what happens to numbers when they are multiplied in the same logarithm 

log(b · c) = log(b) + log(c) 

what happens to numbers when they are divided in the same logarithm 

log(b ? c) = log(b) / log(c) 

what happens to numbers with exponents in a logarithm 

log(ax^{b}) = log(a) + b log(x) 













A general rule for exponents 

x^{a/b} = ^{b}vx^{a} = (^{b}vx)^{a} 


the base10 system the natural system 

base10 system for exponents 


natural system for exponents 


the logarithm of a number is equal to… 


the natural logarithm of a number is equal to… 


how to do log for the base10 rule 

log x = log_{10}(10^{b}) = b 

how to do log for the natural system 

ln x = log_{e} x = log_{e}(e^{a}) = a 

what happens to exponents when numbers are multiplied 

10^{b} · 10^{c} = 10^{b+c}e^{b} · e^{c} = e^{b+c} 

what happens to exponents when numbers go thru division 

10^{b} / 10^{c} = 10^{bc}e^{b} / e^{c} = e^{bc} 

what happens to numbers when they are multiplied in the same logarithm 

log(b · c) = log(b) + log(c) 

what happens to numbers when they are divided in the same logarithm 

log(b ? c) = log(b) / log(c) 

what happens to numbers with exponents in a logarithm 

log(ax^{b}) = log(a) + b log(x) 
