Log Definition/Properties
Using Logs (calc)
Evaluating Logarithms (no calc)
Inverses
Exponents
100
The one word description of a logarithm
A logarithm is an exponent
100
Write an equation where logarithms would be required.
(an equation where x is in the exponent)
100
Provide the exact value of the solution:
3^(2x)=13
x=1/2log_3 13
100
If f(12)=-32 , what do you know about
f^-1(x) ?
f^-1(-32)=12
100
Simplify 5(xy^2)^3
5x^3y^6
200
Rewrite this equation
P=\log_k W
k^P=W
200
Solve for x: 7x=738
What is 3.393?
200
Evaluate
What is 1
200
The graph of a function's inverse is its reflection over which line?
y=x
200
Evaluate (no calc)
25^(5/2)
3125
300
This can be written as the sum and difference of multiple logarithms:
What is:
300
Sketch the graph (include 3 pts.) of
y=\log_5(x)
300
This can be simplified:
What is 0?
300
Find the inverse of
g(x)=100/(2x+7)
g^-1(x)=100/(2x)-7/2
300
Solve
(x+1)^(2/7)=2
x=sqrt(128)-1
400
This can be written as a single logarithm
What is:
400
In 2020, your car was worth $8000. When will its value drop to $7000, assuming that every year it loses 2% of its value?
~6.610 years
400
Evaluate (no calc.)
7^{\log_7 69}
69
400
Find the inverse of
p(x)=11\cdot 3^{2x+5
p^-1(x)=1/2(log_3(x/11)-5)
400
Solve the equation
2^x=64^(x^2-3)
x=-1, 7
500
Write as a single logarithm
2log_3(12)-log_9(4)
log_3(144\cdot sqrt4)=log_9(144^2\cdot 4)
500
You accidentally inhale some toxic fumes. Twenty hours later you go to the doctor and her test results show that the concentration of the toxin is 0.00372 mg/cc. Eight hours later she tests your blood again and records a toxin concentration of 0.00219 mg/cc. When can you leave the hospital, if the acceptable concentration of the toxin is 0.0010 mg/cc?
Assume that the toxin levels decay exponentially with time.
~74.6 hours after initial exposure, or ~48.6 hours after that last test
500
Solve
log_5(25^(x^2))+log_2(32^x)-log_2 (8)=0
x=-3, 1/2
500
Find the inverse of
f(x)=1/2(\log_3(x-1)-\log_3(2))
f(x)=2\cdot3^{2x}+1
500
Solve the equation
3^(x-2)=(1/27)^(4x-3)
x=11/13