# Knowledge Base

## Solution 13902: Algorithm for the Convert Logbase (>logbase) Function on the TI-89 Titanium and Voyage™ 200 with OS v3.10.

### What is the purpose of the convert logbase (>logbase)function on the TI-89 Titanium and Voyage 200 with OS v3.10?

The ►logbase(n) instruction implements the following identity:

loga(b) = logn(b)/logn(a)

Thus, log(8) ►logbase(2) will return log2(8)/log2(10), which simplifies to 3/log2(10) ¡Ö 0.90309... (¡Ö log(8)).

The ►logbase(n) does not change the value of the argument to which it is applied (log(8,2) is not equal to log(8), so one should not expect the ►logbase(2) conversion to return the value of log(8,2) when applied to log(8).

In other words, the instruction does not actually change the base of the given logarithm. Instead, it rewrites the given logarithm as an equivalent expression in terms of logarithms with the user selected base.

For additional instructions, refer to the online guidebook for your Texas Instruments calculator.