Precalc - 3.4(2)Solving Logarithmic Equations

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

What is the inverse relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions. If y = b^x, then x = log_b(y).

Front

How do you solve the equation log_b(x) = c?

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the product rule for logarithms?

Back

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

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What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

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

Front

How do you solve log_5(4x-7) = log_5(x+5)?

Back

Set the arguments equal: 4x - 7 = x + 5. Solve for x to get x = 4.

Front

How do you solve log_4(3x-1) = log_4(2x+3)?

Back

Set the arguments equal: 3x - 1 = 2x + 3. Solve for x to get x = 4.

Front

What is the solution to log_2(x+3) = 4?

Back

Rewrite in exponential form: x + 3 = 2^4. Solve for x to get x = 13.