Exponentials & Logs Flashcards
Where must the variable be so that the function is an exponential?
Variable must be in exponent. Must not be a variable in base
When a > 1 ( a^x) where does the line cross?
When a > 1 all cross y-axis at 1
What type of function is a^x when 0 < x < 1
Decay function
What happens to exponential growth when curve reflected in:
y = 0
x = 0
- Decay curve
- Decay curve
a^b = c
Find b
Log base(a) of (c) = b
What does the exponential curve for y=a^x look like?
When ( a > 1)
& When ( 0 < a < 1 )
Crosses where?
When ( a > 1 ):
- Asymptote with -x axis
- Through (0,1)
- curve upwards with increasing grad to infinity
When ( 0 < a < 1 )
Reflection in Y-axis (of above curve)
What does the exponential curve for
y = log base(a) of (x) look like?
When ( a > 1)
& When ( 0 < a < 1 )
Crosses where?
When ( a > 1 )
- Asymptote with -y axis
- Through (1,0)
- Curve upwards with decreasing gradients to infinity
When ( 0 < a < 1 )
- Reflection in x-axis (of above curve)
Addition and subtraction laws of logs
< = base
log<a(x) + log<a(y) = log<a(xy)
log<a(x) - log<a(y) = log<a(x/y)
k log<a(x) = ?
< = base
log<a(x^k)
Log<10 = ?
Log
Log<a(1) = ?
Log<a(a) = ?
= 0
= 1
