Expanding and Condensing Logs Practice

Front

What is the definition of logarithm?

Back

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

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 does it mean to condense logarithmic expressions?

Back

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

Front

What are the properties of logarithms used for condensing?

Back

The main properties include: 1) log_b(m) + log_b(n) = log_b(m*n), 2) log_b(m) - log_b(n) = log_b(m/n), 3) k*log_b(m) = log_b(m^k).

Front

What does it mean to expand logarithmic expressions?

Back

Expanding logarithmic expressions involves breaking down a single logarithm into multiple logarithms using logarithmic properties.

Front

What is the property of logarithms used for expansion?

Back

The properties used for expansion include: 1) log_b(m*n) = log_b(m) + log_b(n), 2) log_b(m/n) = log_b(m) - log_b(n), 3) log_b(m^k) = k*log_b(m).

Front

How do you condense the expression log_b(m) + log_b(n)?

Back

You can condense it to log_b(m*n) using the property of logarithms.

Front

How do you expand the expression log_b(m^k)?

Back

You can expand it to k*log_b(m) using the property of logarithms.

Front

What is the result of condensing log_8(x) + log_8(y) + 5log_8(z)?

Back

The result is log_8(x*y*z^5) using the properties of logarithms.

Front

What is the result of expanding 6log_8(u) - 2log_8(v)?

Back

The result is log_8(u^6) - log_8(v^2), which can be further expressed as log_8(u^6/v^2).