Write the expression as a sum, difference, or multiple of logarithms.?

Question

Write the expression as a sum, difference, or multiple of logarithms.
Log (base 4) (16x^3/y^2z^4)

Answer 1

Log (base 4) (16x^3/y^2z^4)
= Log(base4) (16) + Log(base4)(x^3) - Log(base4)(y^2) - Log(base4)(z^4)
= Log(base4) (4^2) + 3Log(base4)(x) - 2Log(base4)(y) - 4Log(base4)(z)
= 2Log(base4) (4) + 3Log(base4)(x) - 2Log(base4)(y) - 4Log(base4)(z)
= 2 + 3Log(base4)(x) - 2Log(base4)(y) - 4Log(base4)(z)

Answer 2

2 issues to recollect: Multiplication interior a logarithm is the same undertaking as addition of separate logarithms. branch interior a logarithm is the same undertaking as subtraction of separate logarithms. in this situation, x and y are the two expanded jointly and z is split, so we've: log (xy/z) = log x + log y - log z desire that enables!

Answer 3

The coefficient of 16, being a power of 4, can be moved outside of the log term:
TERM = 2 + log4 ( x3 / (y2* z4))
We can express the denominator product as
(2 log4 y + 4 log4 z)
We can express the numerator as
3 log4 x
Then we can re-express the whole thing as
2 + 3 log4 x - (denom. product )