FLASHCARD - Solving Equations Using Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(x), b is the base.

Front

What is the natural logarithm?

Back

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

Front

What is the relationship between exponents and logarithms?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

How do you solve the equation e^(x+4) = 12?

Back

Take the natural logarithm of both sides: x + 4 = ln(12), then solve for x: x = ln(12) - 4.

Front

What is the definition of log(x) = 1?

Back

This means that x = 10^1, so x = 10.

Front

How do you solve log(x + 6) = 1?

Back

Convert to exponential form: x + 6 = 10^1, so x = 10 - 6 = 4.

Front

What does ln(x) - ln(7) = 0 imply?

Back

This implies that ln(x/7) = 0, so x/7 = 1, thus x = 7.

Front

What is the property of logarithms: log(a) - log(b)?

Back

This property states that log(a) - log(b) = log(a/b).

Front

How do you solve log(2x) - log(5) = 2?

Back

Use the property of logarithms: log(2x/5) = 2, then convert to exponential form: 2x/5 = 10^2, so 2x = 500, thus x = 250.