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:
$\frac{4000(1.5^{x}) }{4000} = \frac{25000}{4000}$
$1.5^{x} = \frac{25}{4}$
Now we can use logarithms to bring down the variable:
$ln(1.5^{x} )=ln( \frac{25}{4})$
$xln(1.5)=ln( \frac{25}{4})$
$x= \frac{ln( \frac{25}{4}) }{ln(1.5)}$
$x=4.52$

Part 2. Lets use the domain (x values) to find the range (y values):
$log_{2} (\frac{1}{2})=-1$
$log_{2} (1)=0$
$log_{2} (2)=1$
$log_{2} (4)=2$
$log_{2} (8)=3$

Finale lets put the points together and draw our graph: