Question 404464
{{{log(7, (75))=x}}}
You mean you don't know what power of 7 is 75? Well, neither do I. So just use the base 7 log button on your calculator!<br>
Just kidding. No one's calculator has a base 7 logarithm button. But it probably does have a base 10 (aka log) button and/or a base e (aka ln) button. So if we can express your base 7 log in terms of base 10 or e logs, we can use our calculator. Fortunately we have the base conversion formula: {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}.<br>
Using the conversion formula we can change to base 10:
{{{log(7, (75)) = log((75))/log((7))}}}
or to base e:
{{{log(7, (75)) = ln(75)/ln(7)}}}
Now we can get out our calculators, find the two logarithms and divide them. And believe it or not, it doesn't matter whether we use base 10 or base e logarithms. They both result in the same answer! (Try then both if you don't believe me.)