Question

Flag question Express log₆z + 2log₆w - 3log₆x in a single logarithm.

Answer 1

To express the expression log₆z + 2log₆w - 3log₆x in a single logarithm, we need to apply the properties of logarithms.

Step-by-step explanation:

To express the expression log₆z + 2log₆w - 3log₆x in a single logarithm, we need to apply the properties of logarithms. The properties we'll use are:

• The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log(xy) = log(x) + log(y)
• The logarithm of a number raised to an exponent: log(x^a) = a * log(x)
• The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log(x) - log(y)

Using these properties, we can rewrite the expression as a single logarithm:

log₆(z) + 2log₆(w) - 3log₆(x) = log₆(z) + log₆(w^2) - log₆(x^3)

Finally, combining the terms using the product and exponent properties of logarithms:

log₆(z) + log₆(w^2) - log₆(x^3) = log₆(z * w^2 / x^3)