You can put this solution on YOUR website! I'm guessing you posted this yesterday and I "solved" it for you. But I misread the problem and solved something else. Sorry about that!
If your problem is to find the number for (or or ), without a calculator, then the answer is: It can't be done! (This leads me to suspect that problem may actually be the problem I thought it was yesterday.)
7 is not a well-known power of 3, 3 is not a well-known power of 7 and both numbers, 3 and 7, are not well-known powers of some other number. One of these would have to be true in order to answer this question without a calculator.
If the 7 was a 9 instead then we could solve this problem because 9 is a well-known power of 3. Since , and
The only thing you can do with your expression is to convert it to an expression of logarithms of a different base. For example, if you did want to use your calculator to find a decimal approximation for the value of your expression, then we could use the base conversion formula for logarithms, to convert your base 3 logarithm into a base that your calculator "knows" like base 10 or base e (aka ln). Converting your base 3 logarithm into base e logarithms we get:
which would make your full expression:
With this we could then use our calculator to obtain a decimal approximation for the value of your expression.
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