To simplify this expression, we will first simplify each individual logarithm term and then combine them.
log3 36 = log3 (3^2 * 4) = log3 3^2 + log3 4 = 2log3 3 + log3 4 = 2 + log3 4
log3 4 = log3 (2^2) = 2 log3 2
log5 8 = log5 (2^3) = 3 log5 2
Substitute these simplified terms back into the original expression:
√5 (2 + log3 4 - 2 log3 2 + 5 * 3 log5 2) / 0.5 log5
= √5 (2 + 2 - 2(1) + 15 log5 2) / 0.5
= √5 (4 - 2 + 15 log5 2) / 0.5
= √5 (2 + 15 log5 2) / 0.5
= 2√5 + 15√5 log5 2
Therefore, the simplified expression is 2√5 + 15√5 log5 2.
To simplify this expression, we will first simplify each individual logarithm term and then combine them.
log3 36 = log3 (3^2 * 4) = log3 3^2 + log3 4 = 2log3 3 + log3 4 = 2 + log3 4
log3 4 = log3 (2^2) = 2 log3 2
log5 8 = log5 (2^3) = 3 log5 2
Substitute these simplified terms back into the original expression:
√5 (2 + log3 4 - 2 log3 2 + 5 * 3 log5 2) / 0.5 log5
= √5 (2 + 2 - 2(1) + 15 log5 2) / 0.5
= √5 (4 - 2 + 15 log5 2) / 0.5
= √5 (2 + 15 log5 2) / 0.5
= 2√5 + 15√5 log5 2
Therefore, the simplified expression is 2√5 + 15√5 log5 2.