SOLUTION: I could really use some help graphing these two functions: f(x)=7^x f(x)= log3x

Algebra ->  Graphs -> SOLUTION: I could really use some help graphing these two functions: f(x)=7^x f(x)= log3x      Log On


   

Question 173334: I could really use some help graphing these two functions:
f(x)=7^x
f(x)= log3x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

In order to graph f%28x%29=7%5Ex, we need to plot some points:


Note: I'll use "y" in place of f(x)



Let's find the y value when x=-2


y=7%5Ex Start with the given equation


y=7%5E%28-2%29 Plug in x=-2


y=%281%2F7%29%5E2 Flip the fraction to make the exponent positive.


y=1%2F49 Square 1%2F7 to get 1%2F49


y=0.02041 Divide


So when x=-2, then y=0.02041


------------------------------------------------------------------


Let's find the y value when x=-1


y=7%5Ex Start with the given equation


y=7%5E%28-1%29 Plug in x=-1


y=%281%2F7%29%5E1 Flip the fraction to make the exponent positive.


y=1%2F7 Raise 1%2F7 to the first power to get 1%2F7


y=0.14286 Divide


So when x=-1, then y=0.14286


------------------------------------------------------------------


Let's find the y value when x=0


y=7%5Ex Start with the given equation


y=7%5E%280%29 Plug in x=0


y=1 Raise 7 to the zeroth power to get 1



So when x=0, then y=1


------------------------------------------------------------------


Let's find the y value when x=1


y=7%5Ex Start with the given equation


y=7%5E%281%29 Plug in x=1


y=7 Raise 7 to the first power to get 7



So when x=1, then y=7


------------------------------------------------------------------


So we have the following values:


xy
-20.02041
-10.14286
01
17




Now let's plot these points





Now draw a curve through those points to graph f%28x%29=%281%2F5%29%5Ex





Note: the graph does NOT cross or touch the x-axis. It just looks like that since the y values become very small.






# 2



In order to graph f%28x%29=log%283%2C%28x%29%29, we need to plot some points:


Note: I'll use "y" in place of f(x)


Let's find the y value when x=1


y=log%283%2C%28x%29%29 Start with the given equation


y=log%283%2C%281%29%29 Plug in x=1


y=0 Use a calculator to evaluate log base 3 of 1 to get 0


So when x=1, then y=0


-----------------------------------------------



Let's find the y value when x=2


y=log%283%2C%28x%29%29 Start with the given equation


y=log%283%2C%282%29%29 Plug in x=2


y=0.63093 Use a calculator to evaluate log base 3 of 2 to get 0.63093


So when x=2, then y=0.63093


-----------------------------------------------



Let's find the y value when x=3


y=log%283%2C%28x%29%29 Start with the given equation


y=log%283%2C%283%29%29 Plug in x=3


y=1 Use a calculator to evaluate log base 3 of 3 to get 1


So when x=3, then y=1


-----------------------------------------------



Let's find the y value when x=4


y=log%283%2C%28x%29%29 Start with the given equation


y=log%283%2C%284%29%29 Plug in x=4


y=1.26186 Use a calculator to evaluate log base 3 of 4 to get 1.26186


So when x=4, then y=1.26186


-----------------------------------------------


Let's find the y value when x=5


y=log%283%2C%28x%29%29 Start with the given equation


y=log%283%2C%285%29%29 Plug in x=5


y=1.26186 Use a calculator to evaluate log base 3 of 5 to get 1.46497


So when x=5, then y=1.46497


-----------------------------------------------




So we have the following values:


xy
10
20.63093
31
41.26186
51.46497




Now let's plot these points





Now draw a curve through those points to graph f%28x%29=log%283%2C%28x%29%29