Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
State the exponential we use for our first table when graphing:
f(x)=-log_6 (x-3)+3
6x
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms:
log_7(49) = x
x=2
Logs written without a base.
Answer in the form "What are __________?"
What are Common Logs?
OR
What are Base 10 Logs?
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
The Domain and Range of a Log function without any transformations.
Domain:
{x|x>0}
Range: All Real Numbers
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms:
log_3(1/27)=
x= -3
Expanding by moving an exponent out, turning it into a coefficient of a log.
What is the Power Rule?
Convert to Exponential Form:
log_(x)(4)=2y
(x)^(2y)=4
List the translations/transformations that happen in:
f(x)=-log_6 (x-3)+3
Reflect along the x-axis
Shift right 3 units
Shift up 3 units
Condense the Logarithms:(use ln the same as any other log)
2log(3)-2log(x)+4log(y)
log((9y^4)/x^2)
Solve by Converting:
log_4(x)=-5
x = 1/1024
Taking the common log of the large number (argument) over the common log of the base.
What is the Change of Base Formula?
Convert to Logarithmic Form:
2^(x+4)=y
log_2(y)=x+4
The end behaviors for
f(x)=log_(1/2) (x+1)-4
As x approaches -1, f(x) approaches infinity.
As x approaches infinity , f(x) approaches negative infinity.
Condense the Logarithms:
3log(x)+4log(2)-5log(z)+3log(3)
log((16x^3)/(27z^5))
Solve using Logarithms:
log_x(1/64) = -2
x = 8
Condensing by taking two logs of the same base that are being added, and writing them as one log with the arguments being multiplied.
What is the Product Property/Rule?
Convert to Exponential Form:
log_(3)(5-z)=4y
(3)^(4y)=5-z
The steps for graphing a logarithm.
1. Make a table for the exponential.
2. Make the inverse table (Log Table)
3. Apply the Transformations.
Completely Expand the Logarithm:
log_7((3x^6y^7)/(z^5))
log_7(3)+6log_7(x)+7log_7(y)-5log_7(z)
Solve using Logarithms:
log_(x+2)(16)=2
x=2
Expanding by taking the difference of the log of a numerator and the log of a denominator.
What is the Quotient Property/Rule?