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Questions and Answers
What is the value of $log_2(3)$ if $log_2 = 0.3$ and $log_3 = 0.48$?
What is the value of $log_2(3)$ if $log_2 = 0.3$ and $log_3 = 0.48$?
- 0.625 (correct)
- 0.5
- 1.6
- 0.75
The change of base formula states that $log_a(b) = \frac{log_c(b)}{log_c(a)}$ for any base $c$.
The change of base formula states that $log_a(b) = \frac{log_c(b)}{log_c(a)}$ for any base $c$.
True (A)
Evaluate $log_2(17)$ using the values $log_2 = 0.3$ and $log_3 = 0.48$. What is the answer?
Evaluate $log_2(17)$ using the values $log_2 = 0.3$ and $log_3 = 0.48$. What is the answer?
1.23
The property of logarithms that states $log_a(xy) = log_a(x) + log_a(y)$ is known as the ______ property.
The property of logarithms that states $log_a(xy) = log_a(x) + log_a(y)$ is known as the ______ property.
Match the following logarithmic expressions with their properties:
Match the following logarithmic expressions with their properties:
What is the value of $log_5(11)$ using the change of base formula?
What is the value of $log_5(11)$ using the change of base formula?
The equation $log_a(b) imes log_b(a) = 1$ is a valid property of logarithms.
The equation $log_a(b) imes log_b(a) = 1$ is a valid property of logarithms.
Evaluate $log_3(8) × log_2(9)$. Provide the answer in terms of logarithms.
Evaluate $log_3(8) × log_2(9)$. Provide the answer in terms of logarithms.
The natural logarithm is denoted as ___.
The natural logarithm is denoted as ___.
Match the logarithmic expressions with their properties:
Match the logarithmic expressions with their properties:
Which graph represents the function $y = 2^x$?
Which graph represents the function $y = 2^x$?
The logarithmic function $y = log_2(x)$ increases as x increases.
The logarithmic function $y = log_2(x)$ increases as x increases.
To evaluate logarithmic expressions with a calculator, one usually uses the buttons for ___.
To evaluate logarithmic expressions with a calculator, one usually uses the buttons for ___.
Which property of logarithms is used to combine the expression $\log_{9}x + \log_{9}x^{2} + \log_{9}x^{3} + \log_{9}x^{4} = 5$?
Which property of logarithms is used to combine the expression $\log_{9}x + \log_{9}x^{2} + \log_{9}x^{3} + \log_{9}x^{4} = 5$?
The equation $\log_{4}x - \log_{4}7 = \frac{3}{2}$ can be simplified using the Quotient Rule.
The equation $\log_{4}x - \log_{4}7 = \frac{3}{2}$ can be simplified using the Quotient Rule.
What is the value of $x$ if $\log_{9}4 + \log_{3}x = 3$?
What is the value of $x$ if $\log_{9}4 + \log_{3}x = 3$?
The equation $\log_{2}x - \log_{8}x = 4$ can be solved by applying the __________ property of logarithms.
The equation $\log_{2}x - \log_{8}x = 4$ can be solved by applying the __________ property of logarithms.
Match the logarithmic equations with their solutions:
Match the logarithmic equations with their solutions:
Which of the following logarithmic identities is incorrect?
Which of the following logarithmic identities is incorrect?
Using a calculator, the natural logarithm can be directly calculated for any given positive number.
Using a calculator, the natural logarithm can be directly calculated for any given positive number.
How would you express $\log_{5}x + 2\log_{5}x$ using the properties of logarithms?
How would you express $\log_{5}x + 2\log_{5}x$ using the properties of logarithms?
Flashcards
Logarithm equation example 1
Logarithm equation example 1
Log₄x - log₄7 = 3/2
Logarithm equation example 2
Logarithm equation example 2
log₉x + log₉x² + log₉x³ + log₉x⁴ = 5
Logarithm equation example 3
Logarithm equation example 3
log₉4 + log₃x = 3
Logarithm equation example 4
Logarithm equation example 4
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Logarithm equation example 5
Logarithm equation example 5
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log₅64 × 2log₄25
log₅64 × 2log₄25
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log₁₀8 × log₂100
log₁₀8 × log₂100
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log 2 = 0.3, log 3 = 0.48, log 17 = 1.23
log 2 = 0.3, log 3 = 0.48, log 17 = 1.23
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a) log₂3
a) log₂3
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b) log₂17
b) log₂17
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Calculate ln(0.2)
Calculate ln(0.2)
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Calculate ln(0.04)
Calculate ln(0.04)
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Calculate log₅(11)
Calculate log₅(11)
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Plot y=2ˣ and y=log₂x on the same axes
Plot y=2ˣ and y=log₂x on the same axes
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Prove logₐb × log♭a = 1
Prove logₐb × log♭a = 1
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Evaluate log₃8 × log₂9
Evaluate log₃8 × log₂9
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Study Notes
Logarithms - Exercise
-
Converting to exponential form: Write logarithmic statements in the form ax = y.
- Example: logmc = d becomes md = c
- Example: logbp = q becomes bq = p
-
Finding the value of x: Solve equations involving logarithms to find the value of x.
- Example: log28 = x becomes 2x = 8 , so x = 3
- Example: logx16 = 0.5 becomes x0.5 = 16, so x = 162 = 256
-
Evaluating logarithmic expressions: Calculate the values of logarithmic expressions.
- Example: log232 = 5, log636=2, log84 = 1.68
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Expressing in terms of loga, logb, logc: Rewrite expressions in terms of these logarithms.
- Example: log(abc) = loga + logb + logc
- Example: loga2bc = 2loga + logb + logc
-
Expressing as a single logarithm: Combine multiple logarithmic terms into one.
- Example: 2log5 + log4 – log10 = log(52 x 4 / 10)
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Converting to log form: Change exponential expressions to equivalent logarithmic expressions.
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Solving logarithmic equations: Find the value of the variable in equations containing logarithms.
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Use of calculator for logarithms: Techniques to find approximate values of x given equations involving logarithms. -Example Find x, if log x=0.32
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Relationship between logarithms: Show that logb×logħa=1
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Graphical representation: Understand logarithmic relationships visually. Plot graphs of logarithmic and exponential functions.
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Solving simultaneous equations with logarithms: Solving systems of equations involving logarithm expressions.
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