b^u=b^v, then u=v
Name two exponential rules. Hint(We learned them in the beginning of the semester)
1) b^u=b^v, then u=v
2) b^-1=1/b
100
What is the natural exponential function?
f(x)=e^x
100
Transfer into log form 2^3=8
Log2 8=3
100
Finish the rest of the property logb uv
logb uv= logb u + longb v
200
27^-2/3
1/9
200
8=1/(16^x)
x=-3/4
200
Name 3 characteristics of the natural exponential function: Domain and Range.
Domain: All reals, Range:0 to infinity, Y int: (0,1), Horizontal at y=0.
200
Change the log into an exponent log3/5 x=2
(3/5)^2=x
200
What is the power rule for logs?
logb u^r= rlogb u
300
y=3^x, find f(-1)
1/3
300
1/(27^x)=(^4√3)^x-2
x=2/13
300
Use your calculator to calculate e^-.534.
0.586
300
Evaluate log log3 1/27
-3
300
Use property to expand expression log2 8x
3+ log2 x
400
A graph lies on the point (2,9/25), find y=b^x
y-(3/5)^x
400
9^x=(1/3)^(x-5)
5/3
400
lne^1/2 Solve
1/2
400
Use properties of logs to evaluate log7^(log7 13)
13
400
expand log6^3
3log6
500
What transformations are in this graph f(x)=-2^(x+1) +3. Sketch graph with two points.
Horizontal shift to the left one, vertical shift up 3, reflection over the x-axis. Points (-1,2), (0,1) & (1,1).
500
Weekly sales will drop rather quickly after the end of an advertising campaign. This drop in sales is known as sales decay. Suppose that the gross sales, S, in hundreds of dollars, of a certain product is given by the exponential function. S(t)=2000(3^-0.2t) Where t is the number of weeks after the end of the campaign. What was the level of sales immediately after the end when t=0? After 1 and 4 weeeks?
t(0)=2000
t(1)=1605
t(4)=830
500
Solve e^(3x-1)=1/√e
x=1/6
500
Find the domain of the log function log5 [(2x-1/x+3)]