Answer:
The value of log(10x/y²) in terms of m and n is (1 - 2m) + (m + 3n).
Explanation:
To find the value of log(10x/y²) in terms of m and n, you can use logarithmic properties.
First, remember the logarithmic rules:
1. log(a) + log(b) = log(a * b)
2. log(a) - log(b) = log(a / b)
3. log(a^n) = n * log(a)
In this case:
log(10x/y²) = log(10x) - log(y²)
Now, apply the properties:
log(10x) - log(y²) = (log(10) + log(x)) - (2 * log(y))
Since log(10) = 1, and you are given that log(x) = m + n and log(y) = m - n, you can substitute these values:
(1 + m + n) - 2 * (m - n)
Now, distribute the -2 inside:
1 + m + n - 2m + 2n
Now, combine like terms:
(1 - 2m) + (m + 3n)
So, the value of log(10x/y²) in terms of m and n is (1 - 2m) + (m + 3n).