1105

• Run Multiple Choice Generator at h:\shares\physics
• Run Core Problems by giving the program 174 as your 'course'--enter this when asked for your 3-digit course number.  
• Do the 'quizzes' on Exponential Functions: Numbers and Exponential Functions: Graphs.
• If you miss a problem be sure to click on Comment and explain what you do and do not understand about the question and the given solution

y = log{base 10}(x) vs. x is inverse to y = 10^x vs. x.  The tables are inverse, the graphs are inverse.  You should be able to make a basic table and graph for both functions in 2 minutes or less.

Make a table of y = 10^x vs. x, then invert it to make a table of y = log{base 10}(x) vs. x. Sketch a quick graph of log{base 10}(x) vs. x.

What are log(100), log(.001) and log(10,000)?

log(100) = 2, easily read from the table.  This happens because 10^2 = 100, which should be clear from looking at both tables.

Similarly, log(.001) = -3 because 10^-3 = .001.

log(10,000) = 4, easily figured by extending the table.  This is so because 10^4 = 10,000.

Estimate log(50), log(-.3), log(.3) and log(7000).

50 lies between 10 and 100, so log(50) lies between log(10) = 1 and log(100) = 2.  We might guess about halfway:  maybe log(50) = 1.5.  This is a pretty good guess.

Looking at the concavity of the graph we see that the actual value is probably a little higher, or about 1.7.

Use your calculator to find log(50), log(-.3) and log(7000).

What is 10^2.4?  What is the log of this number?

What would you get if you took the log of both sides of the equation 10^(2x - 3) = .001?

We would get

• log(10^(2x-3)) = log(.001).

log(10^2.4) = 2.4, log(10^aardvark) = aardvark, and log(10^(2x-3) ) = 2x - 3.

log(.001) = -3, since 10^-3 = .001.

So our equation becomes

• 2x - 3 = -3.

Laws of exponents:

10^(a + b) = 10^a * 10^b

(10^a)^b = 10^(ab).

Laws of logarithms turn these laws around:

log(a * b) = log(a) + log(b)

log(a^b) = b * log(a).