Expand:
log7= 3sqrtx / x^2y
To expand the given expression, log7 = 3√x / x^2y, we need to simplify it further. However, it seems like you're missing an important notation. Here's how you can work with it assuming you meant "log base 7":
$log_7\left(\frac{3\sqrt{x}}{x^2y}\right)$
To expand this expression, let's break it down into smaller parts:
1. Simplify the numerator:
- The square root of x can be expressed as x^(1/2).
- So, we can rewrite the numerator as 3 * x^(1/2).
2. Apply the exponent property of logarithms:
- The numerator can be rewritten as log base 7 of (x^(1/2))^3, using the property log_b(m*n) = log_b(m) + log_b(n).
- This becomes log base 7 of x^(3/2).
3. Simplify the denominator:
- The denominator contains two variables, x^2 and y. We can combine them in the exponent.
- Rewrite the denominator as (x^2 * y)^1.
- This becomes log base 7 of x^(3/2) / (x^2 * y)^1.
4. Further simplify the denominator:
- To simplify (x^2 * y)^1, we can rewrite it as x^2y.
- So the expression becomes log base 7 of x^(3/2) / x^2y.
In summary, the expanded form of the given expression log7 = 3√x / x^2y is log base 7 of x^(3/2) / x^2y.