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