EVALUATING LOGARITHMIC FUNCTIONS
1. log711๐ฅ=43
Solution:
743 =11๐ฅ Transform to exponential form
log743 = log11๐ฅ Apply log to both sides
43log7
log11 =๐ฅlog11
log11 Property of log function
๐๐.๐๐๐ = ๐ Final answer (Rounded to three decimal places)
2. 7log12๐ฅ=21
Solution:
7log12๐ฅ
7=21
7 Simplify
log12๐ฅ= 3
103=12๐ฅ Transform to exponential form
log103= log12๐ฅ Apply log.
3log10
log12 =๐ฅlog12
log12 Property of log
๐. ๐๐๐ = ๐ Final answer (Rounded to three decimal places)
3. log716807
Solution:
log716807 = ๐ฅ Add variable x
7๐ฅ= 16807 Transform to exponential form
7๐ฅ= 75 16807 = (7)(7)(7)(7)(7)= 75
๐ = ๐ Final Answer
4. log51
625 = ๐ฅ
Solution:
5๐ฅ=1
625 Exponential Form
5๐ฅ=1
54 625 =(5)(5)(5)(5)= 54
5๐ฅ= 5โ4
๐ = โ๐ Final Answer
5. log4(2)(8)(1024)= ๐ฅ
Solution:
4๐ฅ=16(1024) Exponential form
4๐ฅ= 42(45) Rewrite as base 4
4๐ฅ= 42+5 Simplify
4๐ฅ= 47 Simplify
๐ = ๐ Final Answer
