Question

Condense each expression to a single logarithm.
4log₃x - 20log₃y

Answer 1

The expression 4log₃x - 20log₃y can be condensed to a single logarithm using the properties of exponents and logarithms. It simplifies to log₃(x^4/y^20).

Step-by-step explanation:

To condense the expression 4log₃x - 20log₃y to a single logarithm, we can use the properties of logarithms that relate exponents and division. First, recall the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. We can apply this to rewrite the given expression as:

log₃(x4) - log₃(y20)

Then, we utilize the property stating that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers:

log₃(4}{y20)

So, the single logarithm equivalent of the given expression is log₃(4}{y20).