Question 313900: can anyone help me with these problems?
1)
express as a single logarithm
loga 7+loga 12
possible solutions:
log2a 84
loga 19
loga 84
log2a 19
2)
Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. State the equation of the line asymptotic to the graph -if any
y = 3x
3)
what is...
logaa^3233
simplified?
4)
Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. State the equation of the line asymptotic to the graph -if any
y = log7 x
5)
The population of a small country increases according to the function
B = 2,400,000e^0.03t, where t is measured in years. How many people will the country have after 4 years?
possible solutions:
3,163,816
2,705,992
5,088,632
2,209,965
6)
There are currently 74 million cars in a certain country, decreasing by 4.3% annually. How many years will it take for this country to have 46 million cars? (Round to the nearest year.) Use the exponential growth model P(t) = P0e^kt. possible solutions:
77 years
11 years
7 years
28 years
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Is this a test, or an assignment for an on-line course? I think this is too many problems for only ONE point. How about I solve the first one for you, and you can repost the others.
By the first law of logarithms, when you add logarithms, you must MULTIPLY like this:
For additional help with Logarithms, please seee my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. There you will see the link to my Homepage. Near the top of my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", and look for "Chapter 4" which is "Logarithms." See Section 4.03, especially page 516-517 for more explanataion on this particular type of problem. In this chapter, you will find my own non-traditional explanation of Logarithms, complete with examples, exercises, and ALL the answers. Many of these exercises are also solved IN COLOR on my "Math in Living Color" pages that go along with these sections.
In addition, please see my FREE videos, which were in my own classes before I retired a few years ago. To see the videos, look on my Homepage for the link "Rapalje Videos in Living Color." Click on "College Algebra" and look for Logarithms Part I and Part II. Probably Part II is appropriate for this question.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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