Express as an equivalent expression, using the individual logarithms of w, x, y, and z.
log(a)(1x^2y^5)
To express log(a)(1x^2y^5) using the individual logarithms of w, x, y, and z, we need to decompose the given term into its factors and rewrite it in terms of those individual terms.
First, let's break down the original expression: log(a)(1x^2y^5)
1x^2y^5 can be written as (1 * x * x * y * y * y * y * y).
Now, we can express each factor in terms of the individual variables:
- The 1 can be written as log(a)(1).
- The x^2 can be written as 2 * log(a)(x).
- The y^5 can be written as 5 * log(a)(y).
So, combining these factors, we get:
log(a)(1x^2y^5) = log(a)(1 * x^2 * y^5)
= log(a)(1) + log(a)(x^2) + log(a)(y^5)
= log(a)(1) + 2 * log(a)(x) + 5 * log(a)(y)
Therefore, the equivalent expression using individual logarithms of w, x, y, and z is:
log(a)(1x^2y^5) = log(a)(1) + 2 * log(a)(x) + 5 * log(a)(y)