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Questions and Answers
What is the value of x in the equation log3(x) = 2?
What is the value of x in the equation log3(x) = 2?
- x = 27
- x = 1/9
- x = 3
- x = 9 (correct)
What is the value of x in the equation log4(x) - log4(2) = 1?
What is the value of x in the equation log4(x) - log4(2) = 1?
- x = 4
- x = 16 (correct)
- x = 8
- x = 2
Solve for x in the equation log2(x) + log2(3) = 3.
Solve for x in the equation log2(x) + log2(3) = 3.
- x = 24 (correct)
- x = 6
- x = 12
- x = 48
Solve for x in the equation 2 * log2(x) = 4.
Solve for x in the equation 2 * log2(x) = 4.
What is the value of x in the equation log2(x) = log3(9)?
What is the value of x in the equation log2(x) = log3(9)?
Solve for x in the equation log3(x) = log2(8).
Solve for x in the equation log3(x) = log2(8).
What is the value of x in the equation log2(x) + log2(x) = 5?
What is the value of x in the equation log2(x) + log2(x) = 5?
Solve for x in the equation log3(x) - log3(2) = 1.
Solve for x in the equation log3(x) - log3(2) = 1.
What is the value of $x$ in the equation $2^x \times 2^{x-1} = 2^5$?
What is the value of $x$ in the equation $2^x \times 2^{x-1} = 2^5$?
What is the value of $x$ in the equation $(3^x)^2 = 3^5$?
What is the value of $x$ in the equation $(3^x)^2 = 3^5$?
What is the value of $x$ in the equation $\(3^x)^2 = 3^5$?
What is the value of $x$ in the equation $\(3^x)^2 = 3^5$?
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Study Notes
Solving Logarithmic Equations
Definition
- A logarithmic equation is an equation involving logarithms, typically in the form:
loga(x) = y - The logarithm is the inverse operation of exponentiation
Properties of Logarithms
loga(M) + loga(N) = loga(MN)loga(M) - loga(N) = loga(M/N)k * loga(M) = loga(M^k)
Solving Logarithmic Equations
Method 1: Using Logarithm Properties
- Use the properties of logarithms to rewrite the equation in a simpler form
- Isolate the logarithm term and apply the inverse operation (exponentiation) to both sides
Example:
log2(x) = 3
2^log2(x) = 2^3
x = 2^3
x = 8
Method 2: Using Exponentiation
- Isolate the logarithm term and raise both sides of the equation to the power of the base (a)
- Simplify the resulting equation
Example:
log3(x) = 2
3^log3(x) = 3^2
x = 3^2
x = 9
Method 3: Using Logarithmic Identities
- Use logarithmic identities, such as
loga(x) = logb(x) / logb(a), to rewrite the equation - Simplify the resulting equation
Example:
log2(x) = log4(16)
log2(x) = log2(16) / log2(4)
x = 16
Common Mistakes
- Forgetting to isolate the logarithm term before applying exponentiation
- Misusing logarithmic properties or identities
- Failing to simplify the resulting equation
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