How do you solve the equation $$log(x+6) = 1$$ ?

To solve, rewrite it in exponential form: $$x + 6 = 10^1$$ , which simplifies to $$x = 4$$ .

How do you simplify $$\frac{m^2y^3}{m^4y^4}$$ ?

By applying the property of exponents, it simplifies to $$\frac{1}{m^{2}y}$$ .

What is the solution to the equation $$log_6(2x - 2) = log_6(5x - 8)$$ ?

Set the arguments equal: $$2x - 2 = 5x - 8$$ , solving gives $$x = 2$$ .

What does $$x^{-n}$$ represent?

It represents the reciprocal of $$x^n$$ , or $$\frac{1}{x^n}$$ .

What is the property of logarithms that states $$log_b(mn) = log_b(m) + log_b(n)$$ ?

This property allows us to express the logarithm of a product as the sum of the logarithms.

What is the property of logarithms that states $$log_b\left(\frac{m}{n}\right) = log_b(m) - log_b(n)$$ ?

This property allows us to express the logarithm of a quotient as the difference of the logarithms.

How do you express $$x^{\frac{7}{9}}$$ with a radical?

It can be expressed as $$\sqrt[9]{x^7}$$ .

What is the solution to $$\frac{1}{x^{\frac{9}{6}}} = x^{\frac{25}{3}}$$ ?

Multiply both sides by $$x^{\frac{9}{6}}$$ to isolate $$x$$ , leading to $$x^{\frac{25}{3} + \frac{9}{6}} = 1$$ .

What is the definition of an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \cdot b^x$$ , where $$a$$ is a constant, $$b$$ is a positive real number, and $$b \neq 1$$ .

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other; if $$y = b^x$$ , then $$x = log_b(y)$$ .

Properties of exponential and log equations practice Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

This property allows us to add the exponents when multiplying two expressions with the same base.

Tags

CCSS.8.EE.A.1

2.

FLASHCARD QUESTION

Front

Back

This property allows us to subtract the exponents when dividing two expressions with the same base.

Tags

CCSS.8.EE.A.1

3.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised, to produce a given number?

Tags

CCSS.HSF.BF.B.5

4.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.5

6.

FLASHCARD QUESTION

Front

What is the definition of a rational exponent?

Back

Tags

CCSS.HSN.RN.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

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