Part 1.] Find the value of x in 4,000( 1.5^(x))=25,000. Show your work. Part 2.] Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation. The grid…

Question

Part 1.] Find the value of x in
`4,000( 1.5^(x))=25,000`. Show your work.

Part 2.] Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation. The grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
`y= log_(2) x`

Answer 1

Part 1. First we are going to divide both sides of the equation by 4000:

`(4000(1.5^(x)) )/(4000) = (25000)/(4000)`

`1.5^(x) = (25)/(4)`
Now we can use logarithms to bring down the variable:

`ln(1.5^(x) )=ln( (25)/(4))`

`xln(1.5)=ln( (25)/(4))`

`x= (ln( (25)/(4)) )/(ln(1.5))`

`x=4.52`

Part 2. Lets use the domain (x values) to find the range (y values):

`log_(2) ((1)/(2))=-1`

`log_(2) (1)=0`

`log_(2) (2)=1`

`log_(2) (4)=2`

`log_(2) (8)=3`

Finale lets put the points together and draw our graph: