What is the property of logarithms that allows you to expand $$\log\frac{x}{y^6}$$ ?

$$\log\frac{x}{y^6} = \log x - 6\log y$$ (Quotient Rule and Power Rule)

Expand the logarithm $$\log(ab)^2$$ using properties of logarithms.

$$\log(ab)^2 = 2\log a + 2\log b$$ (Power Rule and Product Rule)

What does the equation $$\log_x 1000 = 3$$ imply about the relationship between x and 1000?

It implies that $$x^3 = 1000$$ , hence $$x = 10$$ .

Evaluate the logarithm $$\log_2 32$$ .

$$\log_2 32 = 5$$ because $$2^5 = 32$$ .

What is the value of $$\log_2 8$$ ?

$$\log_2 8 = 3$$ because $$2^3 = 8$$ .

How do you solve the equation $$\log x = 2$$ for x?

Convert to exponential form: $$x = 10^2 = 100$$ .

What is the value of $$\log_{10} 1000$$ ?

$$\log_{10} 1000 = 3$$ because $$10^3 = 1000$$ .

If $$\log_3 81 = x$$ , what is the value of x?

$$x = 4$$ because $$3^4 = 81$$ .

What is the value of $$\log_5 25$$ ?

$$\log_5 25 = 2$$ because $$5^2 = 25$$ .

How do you express $$\log_2 16$$ in terms of powers of 2?

$$\log_2 16 = 4$$ because $$2^4 = 16$$ .

Resource Library

Math

Logarithms

Logarithmic Properties

Exponential And Logarithmic Properties Retake

Exponential and Logarithmic Properties Retake

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Mathematics

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11th - 12th Grade

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Practice Problem

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Hard

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CCSS

HSF.BF.B.5

Standards-aligned

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