log(x^3y^2)-2logx*(cubed root of y) - 3log (x/y)

Question

anonymous · Answer

$$logx ^{3}y^{2}+2logx*\sqrt[3]{y}+3\log \frac{ x }{y }$$

anonymous · Answer

seems u want to simplify
in order to solve, we will use the property of log
 $$\log(a^{m})= m* loga$$
$$\log(a*b) = \log a + \log b$$
$$\log(\frac{ a }{ b }) = loga-logb$$

anonymous · Answer

it says write the expression in one logarithm sorry

anonymous · Answer

in order to write in one logarithm , u have to use property of log
i would suggest you to separate the x and y term first or in simple terms just do the simplification first because in the end it will be easy for you to write in single logarithm
for example log(x^3*y^2) = log(x^3) + log(y^2)
                                                = 3logx + 2log(y)
similarly do it for the other two terms ( using the appropriate property)

anonymous · Answer

how do I do it for $$-2logx\sqrt[3]{y}$$  ?

anonymous · Answer

$$-2logx - 2\log(y^\frac{ 1 }{ 3 }) $$

anonymous · Answer

so the 3log x cancels and we have 2logy-3logy-2logx-2logy^1/3