(3x)to the power of lg3 is equal to (4x)to the power of lg4

gobez14 SG

Solve fer x ..

i noe the answer it is 1/12 but how to get!?

pls help

^tamago^ SG

(3x)^{lg 3} = (4x)^lg
4

gobez14 SG

how to get!!!????

^tamago^ SG

(3x)^{lg 3} = (4x)^lg
4

Taking lg,
lg 3 lg 3x = lg 4 lg 4x
lg 3(lg 3 + lg x) = lg 4(lg 4+lg x)
(lg 3)² - (lg 4)² = -lg x(lg 3 - lg 4)
-lg x = lg 3 + lg 4 = lg 12
lg x = lg 12^-1 = lg (1/12)
x = 1/12

gobez14 SG

tahnkew so much tammy

^tamago^ SG

it's okie