Expert: Paul Klarreich - 6/17/2009

Question
Use the properties of logarithms to solve these problems for the value of  x :


1.   log 5 30  +  log 5 2  =  log 5 x

2.   ½ log 6 x  =  log 6 4

3.   log 4 x  –  log 4 5  =  log 4 20

4.   log 3 4 + log 3 x  =  log 3 68

5.   log 7 x  + log 7 (x+ 1) =  log 7 12

6.   log 2 125  =  3 log 2 x

7.   log 9 (2x)  –  log 9 (x – 2) =  log 9 4  
Evaluate each expression, rounding correct to 4 decimal places:

1.   2.34

2.   e5.1

3.   2(5.2)3.1


Find the x-intercept and y-intercept of each graph. State as ordered pairs.

4.   f(x) = 3x – 9

5.   f(x) = ½ x – 1

6.   f(x) =  –2x + 8


The approximate number of fruit flies in a population for a science experiment
after t hours is given by
                                          N(t) = 30e0.05t ,   t ≥ 0

7.   How many fruit flies were there when the experiment started (t = 0) ?

  8.  What will be the population of flies after 40 hours ?  

Answer
Questioner:   gwen
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Precaluclus: exponential function and their graph
Question:  Use the properties of logarithms to solve these problems for the value of  x :
....................................
Hi, Gwen,

This is a lot of questions, so I'll get you started on them, and you can finish up.  Then if you get stuck, send me what you did and I'll try to help.  The symbol ..... means 'take it from here'.

1. log 5 30  +  log 5 2  =  log 5 x

log5(30) = log5(2) = log5(60) .....

2. ½ log 6 x  =  log 6 4

½ log 6 x = log6(sqrt(x)) ......

3. log 4 x  –  log 4 5  =  log 4 20

log4 x  –  log4 5 = log4(x/5) .....

And I think you can handle the next four yourself.

I mean:

And I think you can handle the next for yourself.

4. log 3 4 + log 3 x  =  log 3 68

5. log 7 x  + log 7 (x+ 1) =  log 7 12

6. log 2 125  =  3 log 2 x

7. log 9 (2x)  –  log 9 (x – 2) =  log 9 4  
--------------------------------------------
Evaluate each expression, rounding correct to 4 decimal places:

1. 2.34  ????????

2. e5.1:  e^5.1??  Use your calculator. (Windows has one.)

3. 2(5.2)3.1   ?????


Find the x-intercept and y-intercept of each graph. State as ordered pairs.

x-intercept: Set  y = f(x) = 0, solve for x, write (x,0).

y-intercept: Set  x = 0, solve for y, write (0,y).

and y-intercept

4. f(x) = 3x – 9

5. f(x) = ½ x – 1

6. f(x) =  –2x + 8


The approximate number of fruit flies in a population for a science experiment after t hours is given by N(t) = 30e0.05t ,   t ≥ 0

7. How many fruit flies were there when the experiment started (t = 0) ?

Set t = 0.  I think that gives you 30.


8.  What will be the population of flies after 40 hours ?

Set t = 40.  Use your calculator.