1) This document contains examples of evaluating logarithmic expressions and solving logarithmic equations. 2) Logarithmic expressions are broken down using properties such as loga(bc) = loga(b) + loga(c) and their values are calculated. 3) Logarithmic equations are set up and solved by isolating the logarithmic term and using inverse logarithm properties.

1. (x4)(x7) = x11

2. Find log3 14
= log3 (2)(7)
= log3 2 + log3 7
= 0.6310 + 1.7712
= 2.4022

3. x7
x2 = x5

4. log3 4
= log3 20
5
= log3 20 – log3 5
= 2.7268 – 1.4650
= 1.2618

5. (x4)5 = x20

6. Find log4 36
= log4 62
= 2 log4 6
= 2(1.2925)
= 2.585

7. logb b = 1
log4 4 = 1
log9 9 = 1

8. log3 4 = 1.2618 Find log3 48
= log3 (3)(42)
= log3 3 + log3 42
= log3 3 + 2 log3 4
= 1 + 2(1.2618)
= 1 + 2.5236
= 3.5236

9. Find
= log2 (3)(25)
= log2 3 + log2 25
= log2 3 + 5 log2 2
= 1.5850 + 5(1)
= 6.5850

10. Find

11. Solve
or

12. Solve .

13. Solve
log2 x(x – 6) = 4
x(x – 6) = 24
x2 – 6x – 16 = 0
(x – 8)(x + 2) = 0
x = 8 or x = -2

14. Solve
log3 x2 – log3 62 = log3 4
log3 x2 – log3 36 = log3 4
x2
log3 = log3 4
36
x2
= 4
36
x2 = 144
x = 12 or x = -12