SOLUTION: In the graph y=3^x, read the approximate value of x when y = 5 (1dp) For the graph y=3^(-x), read the approximate value of x when y = 5 (1dp)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: In the graph y=3^x, read the approximate value of x when y = 5 (1dp) For the graph y=3^(-x), read the approximate value of x when y = 5 (1dp)      Log On


   

Question 1048381: In the graph y=3^x, read the approximate value of x when y = 5 (1dp)
For the graph y=3^(-x), read the approximate value of x when y = 5 (1dp)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

 

We draw a green vertical line from the point where y=5 on the
red line where the graph of y = 3x crosses it:



Then we look down at the x-axis and see that the green line
touches the x-axis at a little bit less than 1.5, maybe about 
1.46.  It's actually 1.464973521 which can be calculated with
logarithms.

3%5Ex%22%22=%22%225

Take the logs of both sides:

log%28%283%5Ex%29%29%22%22=%22%22log%28%285%29%29

Use the property of logs log%28%28B%5EA%29%29=B%2Alog%28%28A%29%29 

x%2Alog%28%283%29%29%22%22=%22%22log%28%285%29%29

Divide both sides by log(3)

x%22%22=%22%22log%28%285%29%29%2Flog%28%283%29%29%22%22=%22%220.6989700043%2F0.4771212547%22%22=%22%221.464973521 

If we do the same with the graph of y = 3-x, it just
puts it "in the mirror", i.e., reflects across the y-axis, and
the value of x is just the negative of what it was above.

 

Edwin