Write the logarithmic expression as an expression involving three separate logarithms. (The logarithmic expression is in the description).

Question

log ( ( x ^-8 y^12 z^6 ) ^6 )

Answer 1

Two important log rules are relevant here (these are important enough to commit to memory because they are essential to manipulating logarithms algebraically -- it would also be useful for you to take some time to understand why these properties are true, as they are fundamental to knowing what a logarithm is):

log_b(XY) = log_bX + log_bY

log_b(X^Y) = Ylog_bX

These properties generalize to logarithms of any base (e , 10, etc.). The second follows easily from the first. And the 1st follows from the fact that logs are inverse functions of exponentials. With exponents b^X·b^Y= b^XY

Answer 2

log(x^-48y⁷²z³⁶) = log(x^-48) + log(y⁷²) + log(z³⁶) = -48 log(x) + 72log(y) + 36log(z)

Byanca, hope this makes sense, but let me know--Andrew