Chapter 8

9. Write each expression as a single logarithm.
a) 3 log 5 2 1 log 5 7
d) log 3 12 1 log 3 2 2 log 3 6
C
b) 2 log 3 8 2 5 log 3 2 e)
c) 2 log 2 3 1 log 2 5
f)
log 4 3 1 1 2 log 48 2 log 4 2
2 log 8 1 log 9 2 log 36
10. Use the laws of logarithms to express each side of the equation as a
A
single logarithm. Then compare both sides of the equation to solve.
a) log 2 x 5 2 log 2 7 1 log 2 5 d) log 7 x 5 2 log 7 25 2 3 log 7 5
b) log x 5 2 log 4 1 3 log 3 e) log 3 x 5 2 log 3 10 2 log 3 25
c) log 4 x 1 log 4 12 5 log 4 48 f) log 5 x 2 log 5 8 5 log 5 6 13 log 5 2
11. Write each expression as a single logarithm. Assume that all the
variables represent positive numbers.
a) log 2 x 1 log 2 y 1 log 2 z d) log 2 x 2 2 log 2 xy 1 log 2 y 2
b) log 5 u 2 log 5 v 1 log 5 w e) 1 1 log 3 x 2
c) log 6 a 2 (log 6 b 1 log 6 c) f) 3 log 4 x 1 2 log 4 x 2 log 4 y
1
12. Write as a single logarithm. Assume
2 log ax 1 1 2 log ay 2 3 4 log az
that all the variables represent positive numbers.
13. Describe the transformations that take the graph of f (x) 5 log 2 x to
the graph of g(x) 5 log 2 (8x 3 ).
14. Use different expressions to create two logarithmic functions that have
T the same graph. Demonstrate algebraically why these functions have
the same graph.
15. Explain how the laws of logarithms can help you evaluate log 3 a "5 27
.
2187 b
Extending
16. Explain why log x x m21 1 1 5 m.
17. If log b x 5 0.3, find the value of log b x"x.
18. Use graphing technology to draw the graphs of y 5 log x 1 log 2x
and y 5 log 2x 2 . Although the graphs are different, simplifying the
first expression using the laws of logarithms produces the second
expression. Explain why the graphs are different.
19. Create a pair of equivalent expressions that demonstrate each of the
laws of logarithms. Prove that these expressions are equivalent.
476 8.4 Laws of Logarithms
NEL