Question

Log9 49•log7 5•log25 27•log36 6

Answer 1

Ответ:

225

По шаговое объяснение:

я не знаю

Answer 2

Ответ:

а) log 49 = 2log7

   основания = 9

б) log 27 = 3 log3

   основания = 25

2log 7· log 5 · 3 log 3 · ( log6/log36)=

основание=9; основание=7; основание=25; основания=6=

=3 log 7· (log 5/log7) · ( log 3/log 25)=

=основание=9; основания=5; основания=5=

=3/2·( log 7/log9)· log 3/log 7=3/4

           основание = 5

Answer 3

To simplify the expression, let's evaluate each logarithm separately:

1. log9 49: The base of the logarithm is 9, and the argument is 49. We need to find the exponent to which 9 must be raised to obtain 49. 9^2 = 81, and 9^3 = 729. Since 49 is between 81 and 729, it means that 49 is the square of 9. Therefore, log9 49 = 2.

2. log7 5: The base of the logarithm is 7, and the argument is 5. We need to find the exponent to which 7 must be raised to obtain 5. Since 7 is a prime number, 5 does not have an exact power of 7. Therefore, we can leave this expression as log7 5.

3. log25 27: The base of the logarithm is 25, and the argument is 27. We need to find the exponent to which 25 must be raised to obtain 27. 25^1 = 25, and 25^2 = 625. Since 27 is between 25 and 625, it means that 27 is the cube of 3. Therefore, log25 27 = 3/2.

4. log36 6: The base of the logarithm is 36, and the argument is 6. We need to find the exponent to which 36 must be raised to obtain 6. 36^1 = 36 and 36^2 = 1296. Since 6 is between 36 and 1296, it means that 6 is the square root of 36. Therefore, log36 6 = 1/2.

Now, we can substitute these values back into the expression:

log9 49 • log7 5 • log25 27 • log36 6 = 2 • log7 5 • 3/2 • 1/2

Since log7 5 cannot be simplified further, we leave it as it is:

2 • log7 5 • 3/2 • 1/2 = 3/2 • log7 5

Therefore, the simplified expression is 3/2 • log7 5.