Logarithms 4.3-4.4

Front

Rewrite log_pt = m in exponential form.

Back

p^m = t

Front

If \( \log 2.4 = 0.380211 \), then what is \( \log 2.4 + \log 10^{-7} \)?

Back

-6.619789

Front

Evaluate \( \log_8 \frac{1}{\sqrt{8}} = x \).

Back

-\frac{1}{2}

Front

Expand the logarithm \( \log_5 \frac{x^3}{y^5} \).

Back

3 log₅ x - 5 log₅ y

Front

Solve for x: \( \log_x \left(\frac{1}{8}\right) = -\frac{3}{4} \).

Back

x = 16

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.

Front

State the change of base formula for logarithms.

Back

\( \log_b a = \frac{\log_k a}{\log_k b} \) for any base k.

Front

What is the product rule for logarithms?

Back

\( \log_b (xy) = \log_b x + \log_b y \) for any positive x and y.

Front

What is the quotient rule for logarithms?

Back

\( \log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y \) for any positive x and y.

Front

What is the power rule for logarithms?

Back

\( \log_b (x^k) = k \cdot \log_b x \) for any positive x and k.