Question 283777
{{{log(7, (7^5))}}}
If you understand what logarithms are, you can see what the answer is. In general, {{{log(a, (b))}}} represents the exponent for "a" that results in "b". Your specific logarithm represents the exponent for 7 that results in {{{7^5}}}. And what exponent do you put on 7 to get {{{7^5}}}? Answer: 5, of course!.<br>
Another way to figure this out is to use the property of logarithms, {{{log(a, (p^q))), to move the 5 out in front:
{{{5log(7, (7))}}}
Since {{{log(7, (7)) = 1}}} by definition, this simplifies to 5.<br>
A last resort way to do this is to use the base conversion formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to convert your logarithm into one your calculator "knows". Using this formula to convert your base 7 logarithm into an expression of base 10 logarithms we get
{{{log((7^5))/log((7))}}}
Now you can use your calculator on this. The reasons this is a last resort method are:<ul><li>Calculators use rounded-off decimal approximations for most logarithms. So your calculator may end up telling you the answer is something like 5.00000001 or 4.99999999 instead of the 5 it should be.</li><li>This is longer and more difficult, even with a calculator, than the other methods.</li></ul>