Change of Base Formula

Front

What is the Change of Base Formula?

Back

The Change of Base Formula allows you to convert logarithms from one base to another. It states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

How can you express log_8(64) using the Change of Base Formula?

Back

log_8(64) = log(64) / log(8) using any base k.

Front

What is the equivalent of log_2(16) using the Change of Base Formula?

Back

log_2(16) = log(16) / log(2) = 4.

Front

If log_b(a) = c, what does this imply?

Back

It implies that b^c = a.

Front

What is the value of log_10(1000) using the Change of Base Formula?

Back

log_10(1000) = log(1000) / log(10) = 3.

Front

How do you convert log_3(9) using the Change of Base Formula?

Back

log_3(9) = log(9) / log(3) = 2.

Front

What is the relationship between logarithms of different bases?

Back

Logarithms of different bases can be converted using the Change of Base Formula, allowing comparison and calculation.

Front

What is log_5(25) expressed using the Change of Base Formula?

Back

log_5(25) = log(25) / log(5) = 2.

Front

How can you simplify log_4(64) using the Change of Base Formula?

Back

log_4(64) = log(64) / log(4) = 3.

Front

What is the base change for log_7(49)?

Back

log_7(49) = log(49) / log(7) = 2.