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

How do you solve for x in the equation log(3x + 25) = 2?

Back

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

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 product rule?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n). You can add the logarithms when multiplying the arguments.

Front

What is the value of x if 19^x = 243?

Back

x = 2.5.

Front

How do you simplify 3 ln 5 - ln 2 into a single logarithm?

Back

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

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What does it mean to approximate a solution?

Back

Approximating a solution means finding a value that is close to the exact answer, often used when the exact answer is difficult to calculate.

Front

What is the base of a logarithm?

Back

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

Front

How do you solve the equation 16^(2x) = 124?

Back

Take the logarithm of both sides and solve for x. The approximate solution is x ≈ 0.869.