Question

Solve the equation x=3logy2 for y.

Answer 1

ANSWER
$y = {10}^{ \frac{x}{6} }$


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,



$x =2 \times 3 log( {y} )$


This implies that,

$x =6 log( {y} )$

We now divide both sides by 6 to get,


$\frac{x}{6} =log( {y} )$

We now take antilogarithm to get,


${10}^{ \frac{x}{6} } = y$

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)