Question

Solve the equation x=3logy2 for y.

Answer 1

ANSWER

`y = {10}^{ (x)/(6) }`


Step-by-step explanation

The logarithmic equation given to us is


`x = 3 log( {y}^(2) )`


Recall this property of logarithms,



`log( {a}^(n) ) = n log(a)`




We apply this property to the right hand side to obtain,




`x =2 * 3 log( {y} )`


This implies that,


`x =6 log( {y} )`

We now divide both sides by 6 to get,



`(x)/(6) =log( {y} )`

We now take antilogarithm to get,



`{10}^{ (x)/(6) } = y`

Answer 2

X = 3 · log(Y²)

X = 3 · 2·log(Y)

X/6 = log(Y)

10^(X/6) = 10^log(Y)

Y = 10^(X/6)