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Questions and Answers
Express $log_b(x) + log_b(y) - log_b(z)$ as a single logarithm.
Express $log_b(x) + log_b(y) - log_b(z)$ as a single logarithm.
$log_b(\frac{xy}{z})$
Condense the logarithmic expression: $2log_a(u) + 3log_a(v) - log_a(w)$.
Condense the logarithmic expression: $2log_a(u) + 3log_a(v) - log_a(w)$.
$log_a(\frac{u^2v^3}{w})$
Rewrite the expression $3log(x) + 5log(y)$ as a single logarithm.
Rewrite the expression $3log(x) + 5log(y)$ as a single logarithm.
$log(x^3y^5)$
Combine the following expression into a single logarithm: $4log_m(a) - log_m(b)$.
Combine the following expression into a single logarithm: $4log_m(a) - log_m(b)$.
Condense the expression: $2log_5(x) + 3log_5(4) - 4log_5(2) - log_5(x)$.
Condense the expression: $2log_5(x) + 3log_5(4) - 4log_5(2) - log_5(x)$.
Solve for $x$ by factoring: $x^2 - 5x - 24 = 0$.
Solve for $x$ by factoring: $x^2 - 5x - 24 = 0$.
Solve the quadratic equation $x^2 - 90 = x$ by factoring.
Solve the quadratic equation $x^2 - 90 = x$ by factoring.
Condense: $log_2(y) + log_2(y + 8)$
Condense: $log_2(y) + log_2(y + 8)$
Express $log_3(4) + log_3(y) + log_3(8x)$ as a single logarithm.
Express $log_3(4) + log_3(y) + log_3(8x)$ as a single logarithm.
Rewrite $2loga$ as a single logarithm.
Rewrite $2loga$ as a single logarithm.
Flashcards
Condensing Logarithmic Expressions
Condensing Logarithmic Expressions
Combining multiple logarithmic terms into a single term using properties like product, quotient, and power rules.
Product Rule of Logarithms
Product Rule of Logarithms
logₐ(MN) = logₐ(M) + logₐ(N). Log of a product is the sum of logs.
Quotient Rule of Logarithms
Quotient Rule of Logarithms
logₐ(M/N) = logₐ(M) - logₐ(N). Log of a quotient is the difference of logs.
Power Rule of Logarithms
Power Rule of Logarithms
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Logarithm of the base
Logarithm of the base
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Solving Quadratic Equations by Factoring
Solving Quadratic Equations by Factoring
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Zero Product Property
Zero Product Property
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Study Notes
Here are some study notes for Algebra II B, Properties of Logarithms (Day 1), Assignment 8-2:
Condensing Logarithmic Expressions
- log₄ 5y + log₄ 2y simplifies to log₄ 10y².
- log₂ 9 - log₂ 3 simplifies to log₂ 3.
- 4Logₘ - log n simplifies to log m⁴/n.
- log₇ 5 + log₇ x simplifies to log₇ 5x.
- log₈ x + log₈ y - log₈ z simplifies to log₈ xy/z.
- log₃ 4 + log₃ y + log₃ 8x simplifies to log₃ 32xy.
- 3log x + 5log y simplifies to log x³y⁵.
- log₂ b - log₂ x simplifies to log₂ b/x.
- 2log a simplifies to log a².
- 3log₄ m - 4log₄ 2n simplifies to log₄ m³/16n⁴.
- 2log a + 3log b - 4log c simplifies to log a²b³/c⁴.
- 2log₇ 3 - log₇ 27x simplifies to log₇ 1/3x.
- log₂ y + log₂ (y+8) simplifies to log₂ y² +8y.
- 2log₅ x + 3log₅ 4 - 4log₅ 2 - log₅ x simplifies to log₅ 4x.
Solving by Factoring
- x² - 5x - 24 = 0 factors to x = 8, -3.
- x² - 90 = x factors to x = 10, -9.
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