Question 596154
To find a decimal approximation for a logarithm it must be a logarithm of a base your calculator "knows": base 10 (common) or base r (natural, ln).<br>
So to find a base 7 logarithm you must use the change of base formula to convert it from a base 7 log into base 10 or base e logs. The change of base formula is:
{{{log(a, (p)) = log(b, (p))/log(b, (a))}}}
(Note that the formula converts a log of one base into two logs of another base.)<br>
I'm going to convert the base 7 log into base e logs:
{{{log(7, (988)) = ln(988)/ln(7)}}}<br>
Now just get out your calculator (or computer calculator program) and find the two logs and then divide them. (Important: Do NOT divide 988 and 7 and then find the log. It doesn't work right that way.)<br>
And finally, if we had converted the base 7 log to base 10 logs instead, we would still get the same answer!