Question

Express as a single log: 5logbx + 9logby - 3logbz

a) logb(x⁵y⁹/z³)
b) logb(x⁹y⁵/z³)
c) logb(x⁵y⁹z³)
d) logb(x⁹y⁵z³)

Answer 1

To express 5logbx + 9logby - 3logbza as a single logarithm, we can use the properties of logarithms.

Step-by-step explanation:

To express 5logbx + 9logby - 3logbza as a single logarithm, we can use the properties of logarithms. According to the property that the logarithm of a product is the sum of the logarithms, we can rewrite the expression as:

logb(x^5 * y^9 / z^3)

Using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm, we can simplify further as:

logb((x^5 * y^9) / z^3)

So the answer is option a) logb(x^5 * y^9 / z^3).