You can put this solution on YOUR website!
This expression represents "the power of 9 that results in ". If you're very good with exponents, then you you can figure this our in your head.
If not, then the key to figuring this out is to recognize that both 9 and are both powers of 3: and . Once we realize this, then we would know that converting the base of the logarithm to 3 will make this problem easier.
The base conversion formula is . We can use this to convert our base 9 log to an expression of base 3 logs:
The numerator represents "the power of 3 that results in . We know that this is 1/3. And the denominator represents "the power of 3 that results in 9". This is known to be 2. Substituting these into our expression we get:
which simplifies (by multiplying the top and bottom of the "big" fraction by 3) to:
P.S. Perhaps now you can look back and see how you could have figured this out "the power of 9 that results in " in your head. The power of 9 that results in 3 is 1/2 since 3 is the square root of 9. So we want the exponent for the cube root of the square root of 9:
(