Logarithms Flashcards
Describe relationship between logarithms and exponentials
Inverses of one another
Log multiplication law
log a + log b = log (a x b)
Log division law
log a - log b = log (a/b)
Log power on bracket rule
log (a)^b = b log a
Solving logs rule
log_a(n)=x
Solved via a^x=n
base^ans =what taking log of
Solve log_2(4)=x
2^x=4
x=2
Is it possible to do log of a -ve number
Can’t find the log of a -ve number.
Can’t do log of 0 ei(a) only works for values (a>0)
Natural log
ln(x) = log_e (x)
Special cases (3)
log_a(1/x) = -log_a(x) log_a(a) = 1 (a>0) log_a(1) = 0 (a>0)
Remember to always take constant at front and chnage to a power when solvong equations with logs or will get wrong answer.
Remember to always take constant at front and chnage to a power when solvong equations with logs or will get wrong answer.
Compare the graphs of y=ln (x) and y=e^x
y = ln(x) is a reflection of the graph y=e^x in the line y=x
If says model as a linear linear model
Use y=mx+c as a linear model is a straight line
Log graph y=ax^n
graph of log y against log x will be a straight line with gradient n and y-int log a
(0, log a)
m=n
log graph y=ab^x
graph of log y against x will be a straight line with gradient log b and y-int log a
(0, log a)
Straight line
m=log b
What base is used in log graph questions
base 10 (unless question states otherwise or worked out to be different)
