Question

If (1/12)^x = 2root3, then x is

Answer 1

Step-by-step explanation:

apply log on both sides

log1/12^x = log 2xsqrt3

x log 1/12 = log 2+ log sqrt3

x(log 1 - log12)=log 2 +log 3^½

x(0-log (3×4))=log2 + 1/2 log3

xx(- (log3 + log 2²) = log 2 + log3/2

-x( log3 +2 log2) =(2 log2 + log3)/2

-2x= 2log2 + log3 / log 3 + 2 log2

=1

x=-1/2

alternate explanation:

2×sqrt3 =( 2²x 3)^½ =12^½ = (12^-1)^-1/2= (1/12)^-½= (1/12)^x

x=-½