Logs & Exponentials Flashcards
Logs & Exponential
change to exponential form
logst = v
S^v = t
Logs & Exponential
change to log form
10^2 = 100
log10 100 = 2
What does lne equal?
lne = 1
Solving exponential equations
e.g Solve e^x = 27
lne^x = ln 27
xlne = ln 27
x = ln 27
x = 3.3
Log rules
loga b + loga c
loga bc
Log rules
loga b - loga c
loga b/c
Log rules
loga x^n
nloga x
Log rules
loga 1 = 0
a^0 = 1
Log rules
loga a = 1
a^1 = a
Examples of the rules of log
e.g log10 4 + 2log10 5
log10 4 + log10 5^2
log10 4x25
log10 100
log10 10^2
2log10 10 = 1
= 2
Experimental data
find the values of k & a
step 1 - introduce logs into the equation
(use log from the graph)
step 2 - use rule (1) and (3) to break up the equation
step 3 - match this with the straight line equation (Y = mX + c)
step 4 - find the gradient & y-intercept and match each term
step 5 - you any need to put it together
Log & Exponential graphs
f(x) +- b
exp - a^x +- b
log - loga x +- b
Log & Exponential graphs
f(x +- b)
exp - a^x +- b
log - log a(x +- b)
Log & Exponential graphs
kf(x)
exp - ka^x
log - kloga x
Log & Exponential graphs
f(kx)
exp - a^x
log - loga (kx)
