Logarithm Properties and Solving Exponential and Log Equations

Front

What is the property of logarithms that allows you to condense multiple logs into a single log?

Back

The properties of logarithms, such as the product, quotient, and power rules, allow you to condense multiple logarithms into a single logarithm.

Front

How do you convert a logarithmic equation into its exponential form?

Back

To convert a logarithmic equation of the form \( \log_b(a) = c \) into exponential form, rewrite it as \( b^c = a \).

Front

What is the logarithmic form of the exponential equation \( 3^x = y \)?

Back

The logarithmic form is \( \log_3(y) = x \).

Front

How do you evaluate \( \log_2(32) \)?

Back

Since \( 32 = 2^5 \), \( \log_2(32) = 5 \).

Front

What is the first step in solving the exponential equation \( 4^x - 5 = 12 \)?

Back

The first step is to isolate the exponential term: \( 4^x = 17 \).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that \( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \) for any positive base \( k \).

Front

What is the product rule of logarithms?

Back

The product rule states that \( \log_b(mn) = \log_b(m) + \log_b(n) \).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that \( \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \).

Front

What is the power rule of logarithms?

Back

The power rule states that \( \log_b(m^p) = p \cdot \log_b(m) \).

Front

How do you solve for x in the equation \( 4^x = 17 \) using logarithms?

Back

Take the logarithm of both sides: \( x = \frac{\log(17)}{\log(4)} \).