+8 
1.
We can start by using the properties of logarithms to simplify log_b x^2:
log_b x^2 = 10 2 log_b x = 10 log_b x = 5
Now we can use this result to simplify log_b^(1/3) 1/x:
log_b^(1/3) 1/x = (log_b (1/x))^(1/3)
Next, we can use the property that log_b (1/x) = -log_b x:
log_b^(1/3) 1/x = (-log_b x)^(1/3)
Substituting in the value we found earlier for log_b x:
log_b^(1/3) 1/x = (-5)^(1/3)
We can simplify this using the fact that (-a)^(1/3) = - (a^(1/3)) for any real number a:
log_b^(1/3) 1/x = - (5^(1/3))
So the final answer is -5^(1/3)
+118608
Please just put one question per post.
It is amazing that you got any answer at all. Your questions are all run together and barely readable.
This is how they shouold have been presented, only in 2 different posts.
1. Let x and b be positive real numbers so that \(\log_b(x^2) = 10 \).
Find \(\log_{\sqrt[3]{b}} \left( \frac{1}{x} \right). \)
2. Let a, b, and c be the roots of \(24x^3 - 121x^2 + 87x - 8 = 0\).
Find \(\log_3(a)+\log_3(b)+\log_3(c) \).
