Exponential and logarthmic functions

[NeomiXD]

1. i) For what values of a with the expression log₂a:

a) yield positive numbers?
b) yield negative numbers?
c) yield numbers greater than 1?
d) yield numbers between 0 and 1?
e) be zero?
f) be undefined?


Solution:

1. a) a > 1
b) 0 < a < 1
c) ?
d) ?
e) a = 1
f) a < 0

 

[Mark44]

1. i) For what values of a with the expression log₂a:

a) yield positive numbers?
b) yield negative numbers?
c) yield numbers greater than 1?
d) yield numbers between 0 and 1?
e) be zero?
f) be undefined?


Solution:

1. a) a > 1
b) 0 < a < 1
c) ?
d) ?
e) a = 1
f) a < 0

a, b, e, and f look fine.
For the other two, it would be helpful to sketch the graph of y = log₂x.
(c) For what values of x is y > 1?
(d) For what values of x is y between 0 and 1 (i.e., 0 < y < 1)?

 

[HallsofIvy]

[itex]y= log_2(x)[/itex] is the same as [itex]x= 2^y[/itex].
c) when is [itex]log_2(x)< 0[/itex]?
If y< 0 what is [itex]2^y[/itex]

d) when is [itex]log_2(x)> 0[/itex]?
If y> 0 what is [itex]2^y[/itex]?

 

[Redbelly98]

To the OP: your answer to (e) could help you with answering (c).