Solving Exponentials Using Logarithms

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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 is a logarithm?

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A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number. For example, if b^y = x, then log_b(x) = y.

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How do you convert an exponential equation to a logarithmic form?

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To convert an exponential equation a^b = c to logarithmic form, you write it as log_a(c) = b.

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What is the base of a logarithm?

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The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in log_2(8) = 3, the base is 2.

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What is the change of base formula for logarithms?

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The change of base formula states that log_a(b) = log_c(b) / log_c(a) for any positive c.

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How do you solve an exponential equation using logarithms?

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To solve an exponential equation, take the logarithm of both sides, then use properties of logarithms to isolate the variable.

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What is the property of logarithms that states log_a(m * n) = ?

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log_a(m) + log_a(n) (the product property of logarithms).

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What is the property of logarithms that states log_a(m/n) = ?

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log_a(m) - log_a(n) (the quotient property of logarithms).

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What is the property of logarithms that states log_a(m^n) = ?

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n * log_a(m) (the power property of logarithms).

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Solve for x: 4^(x+2) = 64

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x = 1.