Exponential and Logarithmic Equations

Front

What is the definition of an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent, typically in the form of a^x = b, where a is a positive constant, b is a positive number, and x is the variable.

Front

What is the definition of a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable, typically in the form of log_a(x) = b, where a is the base, x is the argument, and b is the result.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).

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CCSS.HSF.BF.B.5

Front

How do you solve an exponential equation of the form e^(kx) = C?

Back

To solve e^(kx) = C, take the natural logarithm of both sides: kx = ln(C), then solve for x: x = ln(C)/k.

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product property of logarithms?

Back

The product property states that log_a(xy) = log_a(x) + log_a(y).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_a(x/y) = log_a(x) - log_a(y).

Front

What is the power property of logarithms?

Back

The power property states that log_a(x^b) = b * log_a(x).

Front

How do you solve logarithmic equations?

Back

To solve logarithmic equations, isolate the logarithm on one side, convert to exponential form, and then solve for the variable.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.718.