Log(7)8*log(8)7*3^log(9)49

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вопрос

First, let's simplify each part separately:

Log(7)8 = log base 7 of 8
This is asking: 7 raised to what power equals 8?
So, log base 7 of 8 = 3/2

Next, log(8)7 = log base 8 of 7
This is asking: 8 raised to what power equals 7?
So, log base 8 of 7 = 7/3

Finally, 3^log(9)49 = 3 raised to the power of log base 9 of 49
This is asking: 9 raised to what power equals 49?
So, 9^2 = 81

Now, let's calculate the whole expression:

(3/2) (7/3) 81
Simplify further:
(7/2) * 81
Multiply:
567

Therefore, the result is 567.