Podcast
Questions and Answers
What is the value of log10 (1/10000)?
What is the value of log10 (1/10000)?
If log36 6 = x, what is the value of x?
If log36 6 = x, what is the value of x?
Simplify log2 12 - log2 34.
Simplify log2 12 - log2 34.
If log3 5 = 1.465, what is the value of log3 0.6?
If log3 5 = 1.465, what is the value of log3 0.6?
Signup and view all the answers
What is the value of $x$ if $x = \log_3 27$?
What is the value of $x$ if $x = \log_3 27$?
Signup and view all the answers
What does $x = \log_2 (1/4)$ equal to?
What does $x = \log_2 (1/4)$ equal to?
Signup and view all the answers
If $x = \log_5 125$, what is the value of $x$?
If $x = \log_5 125$, what is the value of $x$?
Signup and view all the answers
For $2 = \log_x (16)$, what is the value of $x$?
For $2 = \log_x (16)$, what is the value of $x$?
Signup and view all the answers
What is the rule that relates logarithms in one base to logarithms in a different base?
What is the rule that relates logarithms in one base to logarithms in a different base?
Signup and view all the answers
If log10 3 = 0.47712 and log10 7 = 0.84510, what is log3 7?
If log10 3 = 0.47712 and log10 7 = 0.84510, what is log3 7?
Signup and view all the answers
Given log10 5 = 0.69897, what is log2 5?
Given log10 5 = 0.69897, what is log2 5?
Signup and view all the answers
What is the value of loge 3 if loge 3 = 1.09861?
What is the value of loge 3 if loge 3 = 1.09861?
Signup and view all the answers
Study Notes
Evaluating Logarithms
- The value of log10 (1/10000) is -4, since 10^(-4) = 1/10000.
Properties of Logarithms
- If log36 6 = x, then x = 1/2, since 6^(1/2) = 36.
Simplifying Logarithmic Expressions
- log2 12 - log2 34 = log2 (12/34) = log2 (6/17), by the quotient rule of logarithms.
Logarithmic Equations
- If log3 5 = 1.465, then log3 0.6 = -1.465, since 3^(-1.465) = 0.6.
Exponential Equations
-
If x = log3 27, then 3^x = 27, so x = 3, since 3^3 = 27.
-
If x = log2 (1/4), then 2^x = 1/4, so x = -2, since 2^(-2) = 1/4.
-
If x = log5 125, then 5^x = 125, so x = 3, since 5^3 = 125.
Exponential Equations with Variable Base
- If 2 = logx (16), then x^2 = 16, so x = 4, since 4^2 = 16.
Change of Base Formula
- The rule that relates logarithms in one base to logarithms in a different base is the change of base formula: loga x = logb x / logb a.
Applications of Logarithms
-
If log10 3 = 0.47712 and log10 7 = 0.84510, then log3 7 = (log10 7) / (log10 3) = 0.84510 / 0.47712.
-
If log10 5 = 0.69897, then log2 5 = (log10 5) / (log10 2) = 0.69897 / (log10 2).
-
If loge 3 = 1.09861, then the value of loge 3 is 1.09861.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of logarithms of products with this quiz. Solve problems involving log properties like addition and multiplication. Practice simplifying expressions with logarithms.
