For questions 1 and 2, write the expression as a single logarithm.2 logbq + 8 logbt

Answer 1

To write the expression as a single logarithm, we can use the properties of logarithms.

1) 2 logbq + 8 logbt

We can use the product rule of logarithms, which states that log a + log b = log (a * b):

= logb(q^2) + logb(t^8)

Now, we can use the rule of logb(x) + logb(y) = logb(x * y):

= logb(q^2 * t^8)

Thus, the expression can be written as a single logarithm: logb(q^2 * t^8).

2) 3 logax + 2 logay

Using the product rule of logarithms, we have:

= loga(x^3) + loga(y^2)

Using the rule of loga(x) + loga(y) = loga(x * y), we can simplify further:

= loga(x^3 * y^2)

Therefore, the expression can be written as a single logarithm: loga(x^3 * y^2).