Properties of Logarithms

1. Properties of Logarithms

2. Simplify into a single logarithmic expression: a) log9x4 + 2log3x – 2log2y log9x4 + log(3x)2 – log(2y)2 log9x4 + log9x2 – log4y2 log 9x4∙9x2 4y2 log 81x6 4y2

3. Simplify into a single logarithmic expression:b) 4ln2x + ln(6/x) – 2ln2x ln(2x)4 + ln(6/x) – ln(2x)2 ln16x4 + ln(6/x) – ln4x2 ln 16x4∙6 x∙4x2 ln 96x4 4x3 ln(24x)

4. Expand the following logarithmic expressions: a) = log33x2 – (log39y) = log33 + log3x2 – (log39 + log3y) = 1+ 2log3x – (2 + log3y) = 2log3x – log3y - 1

5. b) = log(y-3)2 – (logy3 + log(x-1)) = 2log(y-3) – 3logy - log(x-1)

6. Let’s do some more challenging questions…Example 1:Given that log34 = x, evaluate log316

7. Example 2:If logma = 3 and logmb = 4, evaluate

8. Example 3:If , determine an expression for logx

9. Example 4:If logx = 3, evaluate log10x2

10. Example 5:If log2A = B, then log4A =?

11. Example 6:If logab = 0.92, then the value of is:

12. Example 7:If log3x = 20, then the value of is:

13. Example 8:If logx = 3.2 and logy = -0.9, then

14. Example 9:logm9 = 2 and log8n = 2, then log2(mn) =

15. Example 10:If x = y2z, then find an expression for logz

16. Example 11:If logbA = M, then

17. Example 12:If 10a = 4, then 101+2a = ?