Question

For the following exercises, condense each expression to a single logarithm using the properties of logarithms.

ln(6x⁹)−ln(3x²)

Answer 1

To condense the expression ln(6x⁹)−ln(3x²) into a single logarithm, we can use the property of logarithms that states the difference of logarithms of the same base can be written as the logarithm of the quotient. The condensed form of the expression is ln(2x⁷).

Step-by-step explanation:

To condense the expression ln(6x⁹)−ln(3x²) into a single logarithm, we can use the property of logarithms that states the difference of logarithms of the same base can be written as the logarithm of the quotient. Using this property, we have:

ln(6x⁹)−ln(3x²) = ln((6x⁹)/(3x²))

Next, simplify the expression inside the logarithm by dividing the numerator by the denominator:

ln((6x⁹)/(3x²)) = ln(2x⁷)

Therefore, the condensed form of the expression is ln(2x⁷).