The expression log a squared over b is equivalent to what
log a - log b :)
To simplify the expression log(a^2/b), we can use logarithmic properties.
1. Start with the given expression: log(a^2/b).
2. Apply the quotient rule of logarithms, which states that log(x/y) = log(x) - log(y):
log(a^2) - log(b)
3. Use the power rule of logarithms, which states that log(x^n) = n*log(x):
2*log(a) - log(b)
Therefore, the expression log(a^2/b) is equivalent to 2*log(a) - log(b).
To determine the equivalent expression of log(a^2/b), we can use logarithmic properties and identities. Here's the step-by-step explanation:
1. Begin by applying the rule of logarithms for division: log(a/b) = log(a) - log(b).
Thus, log(a^2/b) can be rewritten as log(a^2) - log(b).
2. Next, recall the power rule of logarithms: log(a^b) = b * log(a).
Using this rule, log(a^2) can be rewritten as 2 * log(a).
3. Putting it all together, we have log(a^2/b) = 2 * log(a) - log(b).
Therefore, the equivalent expression for log(a^2/b) is 2 * log(a) - log(b).
log(a^2/b) = 2loga - logb
I assume that is what you had in mind, since
(log a)^2 / b does not yield to any simplification
Typing math is always clearer then using just words.