Solving Exponential Functions

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What is an exponential function?

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

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What does it mean to solve an exponential equation?

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To solve an exponential equation means to find the value of the variable that makes the equation true, often by rewriting the equation in terms of the same base.

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How do you rewrite a number as a power of another number?

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To rewrite a number as a power of another number, express it in the form of base^exponent, where the base is the number you want to use and the exponent is determined by how many times the base must be multiplied to equal the original number.

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What is the base in an exponential function?

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The base in an exponential function is the constant 'b' in the expression f(x) = a * b^x, which determines the growth or decay rate of the function.

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What is the exponent in an exponential function?

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The exponent in an exponential function is the variable 'x' in the expression f(x) = a * b^x, which indicates how many times the base is multiplied by itself.

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How do you solve the equation 36 = 6^x?

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Rewrite 36 as 6^2, so the equation becomes 6^2 = 6^x. Therefore, x = 2.

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What is the solution to the equation 16^(2x) = 256^(2x + 5)?

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The solution is x = -5.

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How do you solve the equation 3^3 = 3^(4x + 2)?

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Since the bases are the same, set the exponents equal: 3 = 4x + 2. Solving gives x = ¼.

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What is the solution to the equation 9^(8 - x) = 27^(x - 3)?

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The solution is x = 5.

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What is the property of exponents that allows you to set exponents equal when bases are the same?

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This property states that if a^m = a^n, then m = n, provided that 'a' is not zero.