Question

when I have .5=(0.91)^t, could i do

log(.5)/log(0.91) ?

Answer 1

yes ... that would equal t

Answer 2

Your answer is correct, but you also can write:

log ( x ^ n ) = n ∙ log ( x )

0.5 = 1 / 2 = 1 / 2 ^ 1 = 2 ^ ( - 1 )

log ( 0.5 ) = log [ 2 ^ ( - 1 ) ] = ( - 1 ) * log ( 2 ) = - log ( 2 )

log ( 0.91 ^ t ) = t ∙ log ( 0.91 )


0.5 = 0.91 ^ t

log ( 0.5 ) = log ( 0.91 ^ t )

- log ( 2 ) = t ∙ log ( 0.91 ) Divide both sides by log ( 0.91 )

- log ( 2 ) / log ( 0.91 ) = t

t = - log ( 2 ) / log ( 0.91 )

Answer 3

ok thanks!