Solved Examples on Logarithm Formula
Example 1: Solve log2(x) = 4
Solution:
log2(x) = 4
24 = x
x = 16
Example 2: Solve log2(8) = x
Solution:
log2(8) = x
β 2x = 8
β 2x = 23
β x = 3
Example 3: Find the value of x if log6(x β 3) = 1.
Solution:
log6(x β 3) = 1
β 61 = (x β 3)
β x β 3 = 6
β x = 9
Example 4: Find x if log(x β 2) + log(x + 2) = log21
Solution:
log(x β 2) + log(x + 2) = log21
β log(x β 2) + log(x + 2) = 0 [log(1) =0]
β log[(x β 2)(x + 2)] = 0 [Product Rule]
β (x β 2)(x + 2) = 1 [Antilog(0) = 1]
β x2 β 4 = 1
β x2 = 5
β x = Β±β5 [Log of Negative Number is Not Defined]
β x = β5
Example 5: Find the value of log9(59049).
Solution:
Given log9 (59049) [95= 59049]
= log9(9)5
= 5.log9(9) (identity rule i.e logaa]
= 5
Example 6: Express log10(5) + 1 in form of log10x
Solution:
Given log10(5) + 1
= log10(5) + log1010 [Identity Rule]
= log10(5 Γ 10) [Product Rule]
= log1050
Example 7: Find the value of x if log10(x2 β 15) = 1.
Solution:
log10(x2 β 15) = 1
log10(x2 β 15) = log1010 [Identity Rule]
Applying Antilog,
β (x2 β 15) = 10
β x2 = 25
β x = Β±5
Logarithm Formula
Logarithm was invented in the 17th century by Scottish mathematician John Napier (1550-1617). The Napier logarithm was the first to be published in 1614. Henry Briggs introduced a common (base 10) logarithm. John Napierβs purpose was to assist in the multiplication of quantities that were called sines.
Table of Content
- Logarithm Formula
- Properties of Logarithm
- Product Formula of Logarithms
- Quotient Formula of Logarithms
- Power Formula of Logarithms
- Change of Base Formula
- Other Logarithm Formulas
- Properties of Natural Log
- Product Rule
- Quotient Rule
- Reciprocal Rule
- Log of Power
- Natural Log of e
- Log of 1
- Log Formulas Derivation
Contact Us