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29 Cards in this Set

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a^m × a^n=…
a^(m+n)
a^m / a^n=…
a^(m-n)
(a^m)^n=…
a^(m×n)
a^n × b^n=…
(ab)^n
a^m / b^m=…
(a/b)^m
a^(m/n)=…
(a^(1/n))^m
What is the general form of a simple exponential function?
f(x)=a^x
For very large positive values of x, what value does y approach?
Infinity
For very large negative values of x, what value does y approach?
Zero
Name of the line that a function gets increasingly close to but never reaches?
Asymptote
For all the graphs y=a^x what is the asymptote?
The asymptote is the x-axis
For all the graphs y=a^x what is the y-intercept?
The y-intercept is always (0,1)
When the base is greater than 1 the function…
Increases
When the base is between the values 0 and 1 the function…
Decreases
What is the value of 'e'?
e =2.718….
For y=10^x how can you express the value of x?
x=log y
What is the base of log?
The base is 10
What is the base of ln?
e
log base a of a^x=…
x
a^(log base a of x)=…
x
What is the logarithm of a negative number?
It has no real values
What is the logarithm of zero?
It has no real value
The logarithm of a product (log base a of xy) is…
the sum of the logarithms( log base a of x + log base a of y)
The logarithm of a quotient (log base a of x/y) is…
the difference of logarithms ( og base a of x-y)
The logarithm of a reciprocal (log base a of 1/x) is…
the negative of the logarithm (-log base a of x)
The logarithm of a exponential (log base a ox x^p) is…
the multiple of the logarithm (p log base a of x)
What is the logarithm of 1?
zero
What is the change of base rule?
log base b of a= (log base c of a)/(log base c of b)
For y=log base a of x where does the graph lie?
To the right of the y-axis