logarithms laws

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Revision from previous lesson:

2. Logarithms
By the end of the lesson you will be able to:
• Use the definition of logarithm to prove the
laws for logarithms.
• Apply the laws for logarithms to simplify
expressions.

3. Exercise 4: Verify the following
From worksheet:
log2 4 + log2 8 = log2 32
log3 9 + log3 3 = log3 27
log 100 + log 10 = log 1000
Find a general pattern for loga x+loga y

4. Conclusion:
loga ( x y ) = loga x + loga y
Proof:
loga x = m
loga y = n
⇒
⇒
Use index form:

5. Exercise 4: Verify the following
From worksheet:
log2 64 ­ log2 16 = log2 4
log3 81 ­ log3 3 = log3 27
log5 3125 ­ log5 125 = log5 25
Find a general pattern for loga x ­ loga y

6. Conclusion:
Proof:
loga x = m
loga y = n
⇒
⇒
Use index form:

7. Exercise 4: Verify the following
From worksheet:
Find a general pattern for n loga x

8. Conclusion:
n loga x = loga x n
Proof:
loga x = m ⇒
Use index form:

9. Solve:
log 125 + log 8 =
2 log 5 + log 4 =

10. 3 log3 2 +log3(½) ­ log3 4=

13. Solve Book page 60: Ex 1 to 3 & 6 to 10

14. At the end of the lesson:
loga ( x y ) = loga x + loga y
n loga x = loga x n

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20logs/LogarithmsWriteSingleLogs.html