Exponential and Logarithmic Functions

Front

What is the exponential form of the logarithmic equation \(\log_8 64 = 2\)?

Back

The exponential form is \(8^2 = 64\).

Front

What is the value of \(\log_{20} 20^9\)?

Back

The value is 9.

Front

Solve the equation \(e^x - 8 = 12\) for \(x\) and approximate to three decimal places.

Back

The solution is \(x \approx 2.996\).

Front

Which graph corresponds to the function \(y = 2^x + 3\)?

Back

The graph of \(y = 2^x + 3\) is an exponential growth graph shifted up by 3.

Front

Condense the expression \(\ln x - [\ln(x+6) + \ln(x-6)]\) to a single logarithm.

Back

The condensed expression is \(\ln \frac{x}{(x-6)(x+6)}\).

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is \(e\), approximately equal to 2.718.

Front

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

Back

This property is known as the Product Rule of Logarithms.

Front

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

Back

This property is known as the Quotient Rule of Logarithms.

Front

What is the property of logarithms that states \(\log_b(m^n) = n \cdot \log_b(m)\)?

Back

This property is known as the Power Rule of Logarithms.