Math 115  Lab #9
M. Flashman

I.  Graphs of logarithm Functions
II. Properties of Logarithms

• Tools for Winplot used in this lab:
• explicit
• point
• Families on Inventory.
• Two
• Intersections...

I.Graphs of Logarithm Functions
• Set the parameters: B=2.
• Plot the point (h, B^h)
• Plot the point (B^h, h)
• Plot the point (h,log(B,h))
• Use animator B and  h.
• Plot graphs with explicit for
• y = f(x) = B^x
• y = g(x) = log(B,x)
• y=x
• Use animator B; family B.
• The base of the function g is B
• Graph y = ln(x)
• Graph y = exp(x)

II. Properties of Logarithms
Identity or solve the equation:
Verify the equation is an identity or find all x for which the equation is true:
•  ln(7x) = ln(7) + ln(x)
•  ln(x/5) = ln(x) - ln(5)
•  ln(cos(x)) = - ln (sec(x))
•  ln( 5 + x ) = ln(5)*ln(x)
•  exp(sin(x)) = cos(x)

Record your answers for the next work and submit them on Moodle by Wednesday, April 21st.
Verify the equation is an identity.
If not, find estimates for all solutions in the interval [-6, 6]

1. ln(x-4) = ln(x) - ln(4)
2. ln(x^5) = 5 ln(x)
3. ln(tan(x)) = ln(sin(x)) - ln(cos(x))
4. ln(sqrt(x) ) = 0.5*ln(x)
5. exp(cos(x)) = sin(x)
6. ln( 3* 5^x) = ln(3) + ln(5)*x
7. ln( 5* x^3) = ln(5) + 3*ln(x)

End of Lab 9