You can put this solution on YOUR website! I'm guessing that the expression is which means 3 to the base 3 log of 8
What you posted means 3 to the base 10 log of which is not the same as 3 to the base 3 log of 8.
Logarithms of bases other than 10 or e are difficult to post because the base is written like a subscript. One way to post your expression would be
3^(base 3 log of 8)
Another way would be to post it the way I am getting the expressions to look like they do. Click on the "Show source" link just above this solution and you can see what I typed.
If I am right about your expression then the answer is very easy once you understand what a logarithm is. The idea behind logarithms is this: You can take any positive number except 1 and, if youraise it to the right power, get any positive number. Some of these powers are well-known. For example:
You can raise 4 to the 2nd power to get 16
You can raise 4 to the 1/2 power to get 2 (a 1/2 exponent means square root)
You can raise 4 to the -1 power to get 1/4
etc.
Many of these "right powers" are difficult to know. For example what power of 4 results in a 5? What power of 13 results in 1/3? etc.
Logarithms are used to express these exponents, both the well-known and the unknown. In general represents the exponent you use on "a" to get "p". Some specific examples: is the exponent for 4 that results in 16. We know this one. It is 2. So . represents the exponent for 100 that results in 10. We know this one, too. It is 1/2. So represents the exponent for 41 that results in 64. This one we don't know.
So the logarithm in your expression, represents the exponent for 3 that results in 8. This is another one we don't know. But look at where it is! It iis the exponent on a 3! So your expression is raising 3 to the power which, when it is the exponent on a 3, which results in 8. IOW, your expression is 3 to the power for 3 that results in 8. So by the very definition of what logarithms mean: !!
In general for all valid a's and p's.
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