Given u = log(x) and v = log(y). Express log
(y^2/^3√x^4)
in terms of u and v.

Question

Given u = log(x) and v = log(y). Express log
(y^2/^3√x^4)
in terms of u and v.

shiraz14 · Answer

Could you please re-write the equation using the Equation function (I presume there is something amiss with the denominator)? Thanks.

anonymous · Answer

$$\frac{ Y^{2} }{ \sqrt[3]{x^4} }$$

anonymous · Answer

@shiraz14

shiraz14 · Answer

$$\log(\frac{ y^{2} }{ \sqrt[3]{x^{4}}}) = 2\log(y) - \frac{ 4 }{ 3 }\log(x) = 2v - \frac{ 4 }{ 3 } u$$

anonymous · Answer

so what exactly did you do?

shiraz14 · Answer

Basically we use the following identities:
1. log(a/b) = log(a) - log(b)
2. log(a^b) = blog(a)

And you'd need to convert the root to an exponential - i.e. the cuberoot of x = x^(1/3), for instance.

anonymous · Answer

alright thanks its it a bit confusing but ill figure it out with some practice

shiraz14 · Answer

YW