Question

write as the sum and/or difference of logarithms. express powers as a factor.
log4(√x/64)
answer choices are
a) log4^(x-3
b) -3log4^x
c) 12-(1/2)log4^x
d) (1/2)log4^(x-3)

Answer 1

Since it is a quotient, we'll express as a difference:
log4(√x/64) = log4(√x) - log4(64)
log4(√x/64) = log4 (x)/2 - log4 (4^3)
log4(√x/64) = log4 (x)/2 - 3

Answer 2

You have a few of these questions posted. Just to let you know the rules of logs, which will answer all these questions \[\log A +\log B = \log AB\] \[\log A - \log B = \log \frac{A}{B}\] \[\log A^C = C \log A\] \[\log_x A = n \textrm{ means that } x^n=A \]