Question

given 2logx + 3 logy =0,express y in terms of x

Answer 1

Step-by-step explanation:

the solution is as follows

Answer 2

Answer:

Required answer is $y = {x}^{ -\frac{2}{3} }$

Step-by-step explanation:

Given,$2 log(x) + 3 log(y) = 0$

Here we want to express y in terms of x.

first we are separating $log(x)$and $log(y)$

$2 log(x) = -3 log(y) ......(1)$

We know by logarith $log( {a}^{b} ) = b \: log(a)$

So,$2 log(x) = log( {x}^{2} )$

and -$3 log(y) = log( {y}^{-3} )$

From equation (1),

$log( {x}^{2} ) = log( {y}^{-3} ) ......(2)$

Again

$log(a) = log(b) \\ a = b$

From equation (2),

${x}^{2} = {y}^{-3} \\ y = { x }^{ {2}^{ (-\frac{1}{3} )} } = {x}^{ -\frac{2}{3} }$

Some extra Logarithm formula,

$log_{x}(1) = 0 \\ log_{x}(0) = 1 \\ log_{x}(y) = \frac{ log(x) }{ log(y) } \\ log( {x}^{y} ) = y log(x) \\ log(x) + log(y) = log(xy) \\ log(x) - log(y) = log( \frac{x}{y} ) \\ log_{x}(x) = 1$