EBER - Math 3 wk 6

Front

What is a logarithm?

Back

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

Front

What is the Power Property of Logarithms?

Back

The Power Property states that log_b(a^c) = c * log_b(a). This means you can bring the exponent in front of the logarithm.

Front

If log(3x + 25) = 2, how do you solve for x?

Back

To solve for x, rewrite the equation in exponential form: 3x + 25 = 10^2. Then solve for x.

Front

What is the value of 10^2?

Back

10^2 = 100.

Front

How do you isolate x in the equation 3x + 25 = 100?

Back

Subtract 25 from both sides: 3x = 75. Then divide by 3: x = 25.

Front

What is the natural logarithm?

Back

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

Front

How do you combine logarithms using the Quotient Rule?

Back

The Quotient Rule states that log_b(a/c) = log_b(a) - log_b(c). You can subtract the logs when dividing.

Front

What is the result of 3 ln 5 - ln 2 as a single natural logarithm?

Back

Using the properties of logarithms, it simplifies to ln(5^3 / 2) = ln(125 / 2) = ln(62.5).

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. For example, in log_b(a), b is the base.

Front

What does it mean if log_b(a) = 0?

Back

If log_b(a) = 0, it means that a = 1, because any number raised to the power of 0 equals 1.