Logarithm Properties and Identities

The video tutorial introduces a logarithm property, demonstrating how to substitute and simplify expressions, raise them to exponents, and equate different expressions. It derives a useful logarithm identity, explaining its application in calculators for bases not directly supported. The tutorial emphasizes understanding and practical use of this identity.

What is the relationship between x^n = a and log base x of a = n?

• They are unrelated.

• They are equivalent expressions.

• One is the inverse of the other.

• They are contradictory.

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CCSS.HSF.BF.B.5

What happens when you substitute n with log base x of a in the expression x^n = a?

• The expression becomes a constant.

• The equation becomes invalid.

• The expression becomes x^(log base x of a) = a.

• The expression simplifies to x = a.

Tags

CCSS.HSF.BF.B.5

What is the result of raising both sides of the equation x^(log base x of a) = a to the power of 1 over log base x of a?

• The equation becomes x = a.

• The equation becomes a constant.

• The equation becomes x = 1.

• The equation becomes a = 1.

Tags

CCSS.HSF.BF.B.5

How can you express x in terms of another variable b?

• x = b^(log base b of x)

• x = b^(log base x of b)

• x = b^(1 over log base x of b)

• x = log base b of x

What is the result of setting a^(1 over log base x of a) equal to b^(1 over log base x of b)?

• a = b

• a^(log base x of b) = b^(log base x of a)

• a^(1 over b) = b^(1 over a)

• a^(log base x of a) = b^(log base x of b)

What is the logarithm identity derived from a^(1 over log base x of a) = b^(1 over log base x of b)?

• log base a of b = log base x of a / log base x of b

• log base a of b = log base b of x / log base a of x

• log base a of b = log base x of b / log base x of a

• log base a of b = log base x of a * log base x of b

Why is the derived logarithm identity useful for calculators?

• Calculators cannot compute logarithms.

• Calculators can compute logarithms in any base.

• Calculators can only compute logarithms in base 10 or base e.

• Calculators can only compute logarithms in base 2.

How can you calculate log base 7 of 3 using a calculator?

• By dividing log base 10 of 3 by log base 10 of 7.

• By multiplying log base 10 of 3 by log base 10 of 7.

• By subtracting log base 10 of 7 from log base 10 of 3.

• By adding log base 10 of 3 to log base 10 of 7.

What is the main purpose of the video tutorial?

• To introduce a new logarithm base.

• To derive and explain a useful logarithm identity.

• To solve complex logarithm equations.

• To demonstrate the history of logarithms.

What is the significance of the identity log base a of b = log base x of b / log base x of a?

• It is only useful for theoretical mathematics.

• It provides a method to solve exponential equations.

• It simplifies logarithmic expressions to a single base.

• It allows for the calculation of logarithms in any base using a calculator.