Question

Write as the sum and/or difference of logarithms. Express powers as factors log(7)(xy^2/z^3)

Answer 1

To express log7(xy^2/z^3) as a sum and/or difference of logarithms, one can apply the properties of logarithms for products, quotients, and exponents to break down the expression into log7(x) + 2log7(y) - 3log7(z).

Step-by-step explanation:

The expression log7(xy2/z3) can be written as the sum and/or difference of logarithms using logarithmic properties. To do so, we use the following steps:

1. Apply the property that the logarithm of a product equals the sum of the logarithms: log7(xy2) = log7(x) + log7(y2).
2. For the division, use the property that the logarithm of a quotient is the difference between the logarithms of the numerator and the denominator: log7(xy2) - log7(z3).
3. Finally, apply the property for exponents, which states that the logarithm of a number raised to an exponent is the exponent multiplied by the logarithm of the base number: log7(x) + 2log7(y) - 3log7(z).

By using these properties, the expression is simplified to its sum and/or difference of logarithms form.