Condensing & Expanding Logarithms

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 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(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

Condense: log_8(x^6) - log_8(y^3)

Back

log_8(x^6/y^3)

Front

Expand: log_8(xy^5)

Back

log_8(x) + 5*log_8(y)

Front

Condense: 15*log_8(u) - 3*log_8(v)

Back

log_8(u^15/v^3)

Front

Expand: log_8(xyz)

Back

log_8(x) + log_8(y) + log_8(z)

Front

What is the definition of condensing logarithms?

Back

Condensing logarithms involves combining multiple logarithmic expressions into a single logarithm using the properties of logarithms.