Final answer:
To simplify the given expression, we can combine the logarithms using the properties of logarithms and then simplify further by applying the rules of logarithms.
Step-by-step explanation:
To simplify the expression 5logu+logv-9logw, we can use the properties of logarithms. First, we can combine the logarithms using the rule log(a) + log(b) = log(ab). So, the expression becomes log(u^5) + log(v) - log(w^9).
Next, we can use the rule log(a^b) = b * log(a) to simplify further. So, now the expression becomes log(u^5 * v) - log(w^9).
Finally, using the rule log(a) - log(b) = log(a/b), we can write the expression as log((u^5 * v) / w^9). This is the simplified form of the given expression.