How does the phrase "send the base to the basement". refer to the change of base formula?
the change of base involves a fraction with logs both top and bottom.
log N is on top, and
log b is below
where the log is in any other base.
That is,
log N / log b = logbN
Thank you.
The phrase "send the base to the basement" is a mnemonic device that helps people remember the concept of the change of base formula in mathematics, particularly when working with logarithms.
In mathematics, logarithms are used to solve equations involving exponents. The most common logarithms are the base 10 logarithm (written as log) and the natural logarithm with base e (written as ln).
Sometimes, we encounter logarithms with bases that are not 10 or e. This is where the change of base formula comes into play. The formula allows us to convert a logarithm with any base to a logarithm with a different base. The typical form of the change of base formula is:
log(base a) x = log(base b) x / log(base b) a
Now, let's relate this formula to the phrase "send the base to the basement."
The phrase "send the base to the basement" is a memorable way to remind us that when using the change of base formula, we need to "send" the original base (base a) "to the basement" by taking its logarithm with a different, more common base (base b).
In other words, when we want to convert a logarithm with base a to a logarithm with base b, we "send" base a to the denominator of the formula and take its logarithm with base b in the numerator.
By following this phrase, we can remember the steps to use the change of base formula in order to solve logarithmic equations with different bases.