Log/Exp Basics
Properties of Logs
Common/Natural Logs
Solving
More Solving
200
Rewrite this in exponential form.
200
log((x^2*y)/sqrt(z))
Expand the logarithmic expression using properties.
2logx+log(y)-(1/2)log(z)
200
This number is the base of the Natural Logarithm
What is e or Euler's number (2.718281828)
200
This can be simplified without a calculator to get full credit.
log_9 x=1/2
What is 3
200
log3(x)+log3(x+8)=2
x=1
300
The one word description of a logarithm
exponent or power
300
Condense this into a single log:
4log2A+6log2B
What is log2A4B6
300
log(10x+4)=log(25x)
x=4/15
300
Solve for x:
7x-5=117644
x=6
300
Plutonium-241 decays according to the function A(t)=A_0e^(-0.053t) where t is the time in years. Find the half life if you start with 500 g.
What is 13.08 years
400
A logarithmic function is the inverse of an __________ function.
What are Exponential Functions
400
This can be written as a single logarithm
What is:
400
ln(e^9) is this.
What is 9?
400
Solve for x:
-5+log_5 (8-3x)=-2
x=-39
400
A midwestern city with a population of 1 million finds its population is increasing at a rate of P(t)=P_0e^(0.4t) how long will it take for the population to reach 2.3 million people?
What is 2.1 years
500
Express in log form: 9x=50
What is log950=x
500
This can be written as the sum and difference of multiple logarithms:
What is:
500
This has an exact value:
What is 1/3
500
Solve for x: Round to 3 decimal places
log (9x-5)=3+log(x-2)
What is x=2.023
500
Solve for x: Round answer to 3 decimal points
3^(x-4)=7^(2x+5)
What is: -5.057
600
Express in exponential form:
log_12 x=5
What is
12^5=x
600
This is a property of logarithms and has a value:
What is zero
600
The vertical asymptote of
y=log_5(x+3)
x=-3
600
Solve for x:
logx+log(x-1)=log(4x)
only x=5
600
(1/3)^(2x-1)=27^(x+1)
x=-2/5