12 Questions
What is the value of log10 (1/10000)?
-4
If log36 6 = x, what is the value of x?
12
Simplify log2 12 - log2 34.
-4
If log3 5 = 1.465, what is the value of log3 0.6?
-0.465
What is the value of $x$ if $x = \log_3 27$?
3
What does $x = \log_2 (1/4)$ equal to?
-1
If $x = \log_5 125$, what is the value of $x$?
3
For $2 = \log_x (16)$, what is the value of $x$?
4
What is the rule that relates logarithms in one base to logarithms in a different base?
loga c = loga b × logb c
If log10 3 = 0.47712 and log10 7 = 0.84510, what is log3 7?
1.77124
Given log10 5 = 0.69897, what is log2 5?
2.32193
What is the value of loge 3 if loge 3 = 1.09861?
1.09861
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.
Test your understanding of logarithms of products with this quiz. Solve problems involving log properties like addition and multiplication. Practice simplifying expressions with logarithms.
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