Solved Questions using Change of Base Formula
Question 1: Evaluate log648 using the change of base formula.
Solution:
log648 = {log 8}/{log 64}
⇒ log648 = log 8/ log 82
Using the property log am = m log a, we have:
⇒ log648 = log 8/ 2 log 8
⇒ log648 = 1/2
Question 2: Evaluate log119.
Solution:
Using the change of base formula, we have:
log119 = log 9/ log 11 = 0.95452/1.0413 = 0.91667
Question 3: Evaluate log98.
Solution:
Using the change of base formula, we have:
log98 = log 8/ log 9 = 0.90308/0.95424 = 0.9464
Question 4: Evaluate log1110.
Solution:
Using the change of base formula, we have:
log1110= log 10/ log 11 = 0.8655/0.57849 = 0.8755
Question 5: Evaluate log65.
Solution:
Using the change of base formula, we have:
log65 = log 5/ log 6 = 0.8982
Question 6: Evaluate log43.
Solution:
Using the change of base formula, we have:
log43 = log 3/ log 4 = 0.7924
Question 7: Evaluate log87.
Solution:
Using the change of base formula, we have:
log87 = log 7/ log 8 = 0.9357
Change of Base Formula
The change of base formula is a useful concept in mathematics. Especially when dealing with logarithms, It allows you to convert a logarithm from one base to another. Change of base formula in logarithm allows us to rewrite a logarithm with a different base. Instead of calculating the logarithm directly with the given base, we can use a different base and adjust the formula accordingly.
The significance of the change of Base Formula lies in its practical applications. It allows us to compute logarithms using calculators or computational tools that may only support logarithms with certain bases, typically base 10 (log10) or natural logarithms (ln). This formula is also useful in solving equations involving logarithms, simplifying expressions, and proving various mathematical identities.
Table of Content
- Change of Base Formula
- Base Change Formula of Log
- Derivation of Change of Base Formula
- Properties of Log Change of Base
- Solved Questions using Change of Base Formula