What is the solution to the equation $$3^3 = 3^{4x + 2}$$ ?

The solution is $$x = \frac{1}{4}$$ .

How do you rewrite $$81^{3-x} = (1/3)^{5x-6}$$ in terms of the same base?

Rewrite as $$3^{4(3-x)} = 3^{-1(5x-6)}$$ .

What is the base of the exponential function in the equation $$y = a^x$$ ?

The base is $$a$$ , which must be a positive real number.

How do you solve $$a^x = b$$ for x?

Take the logarithm of both sides: $$x = \frac{\text{log}(b)}{\text{log}(a)}$$ .

What is the inverse operation of an exponential function?

The inverse operation is the logarithm.

What is the definition of an exponential function?

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

What is the significance of the base in an exponential equation?

The base determines the rate of growth or decay in the exponential function.

Resource Library

Math

Algebra

Exponential Equations

Solve Exponential Equations

Flashcard

•

Mathematics

•

11th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.A.1, HSF.BF.B.5, HSF.BF.B.3

Standards-aligned

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FLASHCARD QUESTION

Front

What is the general form of an exponential equation?

Back

FLASHCARD QUESTION

Front

How do you solve an exponential equation with the same base?

Back

To solve an exponential equation with the same base, set the exponents equal to each other and solve for the variable.

FLASHCARD QUESTION

Front

What is the value of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1.

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