Exponents and Logs

Exponential graphs intersect at:

(0,1)

Growth questions equation:

A= P (1+i)^n A= end amount P= beginning amount I= rate of change N= time

In exponential functions, the variable is where?

Exponent

True False: Exponential graphs have x-intercepts.

False

True False: It says condense, you have to take out all logs.

False. It just means simplify, leave a log.

Convert 16=4^2 to logarithmic

log4^16= 2

If there is no base, what base do all logs have ?

10

Solve means

Get x by itself. (no logs)

In a 'growth' graph the base is:

Greater than 1

Reciprocal exponent:

If x is the base and it has an exponent, raise both sides to the reciprocal of that exponent. Ex. x^2= 16 --> 1/2(x^2)= 1/2(16) ---> x=8

Change of Base Rule:

In logs, divide number by base. Big number divided by little number.

Logarithmic function is the _____ of an exponential function.

Inverse

In a 'decay' graph the base is:

Less than 1

On a log function, the base can never be:

Negative, 0 or 1

When theres no way to get a common base what do you do?

Solve with logs

Richter Scale questions:

Subtract the larger earthquake from the smaller one then raise 10 to the difference.

How do you solve using logs?

Take the logs of each side. Simplify using Laws of Logs. When you achieve two logs with no extra terms, cancel the logs and solve for x algebraically.

Power Law:

When there is an exponent in a log, move it to the front to be a coefficient.

Multiplication Law:

When logs are being added, multiply them.

Division Law:

When logs are being subtracted, divide them.

Substitution

When there is a big equation, everytime you see a 'logx' just put x, and solve normally. Remember to put the logs back in at the end.

Grouping

When there is more than 2 terms with logs, simplify using the Laws of Logs until there is only one log term with a variable in it. Isolate the variable, then simplify and solve using the Laws of Logs

In exponential graphs, what is the domain?

XER

What do you do once you achieve a common base?

forget the bases and solve for x using only the exponents.

Exponential graphs have ______ asymptotes

horizontal

Half life

how long it takes for the quantity to reduce to half.

Log graphs have a ____ asymptote

vertical. (x=0)

Convert log(0.2(x)) to exponential

x=0.2^y

the equation for a horizontal asymptote is:

y=0

Range of an exponential graph is:

y> wherever it levels off (vertical translation value is your range)