Specify the interval that the value of the expression belongs to 5log7 36 * log6 49 + 12 ^ log12 5

Find the value of the expression.

5log7 36 * log6 49 + 12 ^ log12 5 =
5 * (log7 6 ^ 2) * (log6 7 ^ 2) + 12 ^ log12 5.

We take out exponents for the sign of the logarithm; we apply the property of the logarithm a ^ loga b = b for the last term:

5 * 2 * (log7 6) * 2 * (log6 7) + 5.

We swap the number and base in the first logarithm:

20 * (1 / (log6 7)) * (log6 7) + 5 = 20 +5 = 25.

Answer: 25.