10 points easy earn?

Question

rewrite the expression
log base 2 of x +3 log base 2 of y - 5 log base 2 of z
as a single logarithm log bas 2 of A

it said it wrong please help

Answer 1

First rule of logs:
k log x = log (x^k)

So that simplifies your equation to:
log[2] x + log[2] (y^3) - log[2] (z^5)

Next rules are:
log a + log b = log(ab)
log c - log d = log(c/d)

Your final equation should be:
log[2] ( x y^3 / z^5 )

Answer 2

log(base 2) (x) + 3 log(base 2) y + log(base 2) z^-5

= log(base 2) (x)(y^3)(z^-5) (rule : log(a)(b) = log a + log b)
(rule : log a^b = b log(a))


= log(base 2) xy^3/z^5)

Answer 3

in base 2:

= log x + 3log y - 5log z
= (base 2) log (xy^3)/(z^5)

Hope this helps :)