Question

I need an expression written for the following logs using "sum, difference, or multiple of logarithms."

a) log[base(2)] ((x^2) - 9)/(x^3))^3

b) log[base(a)]5a^4

Hopefully they are clearly written.

thanks.

-roberto

Answer 1

the base doesn't really matter. All logs follow the same rules.

(a) log(x^2-9) - 9log(x)
but your parentheses are not balanced, so that's a guess. Could also be

3(log(x^2-9) - 3log(x))

(b) log(5) + 4log(a)
Now, it helps to know that we're using logs base a, since then we have
log_a(5) + 4