Question

Log81 1/9= need help with this

Answer 1

`log_(81)(\frac{1}9})`

`81^(x) = (1)/(9)`

`ln(81^(x)) = ln((1)/(9))`

`x\ln(81) = ln((1)/(9))`

`(x\ln(81))/(ln(81)) = (ln((1)/(9)))/(ln(81))`

`x = (ln((1)/(3))^(2))/(ln(3)^(4))`

`x = (2ln((1)/(3)))/(4ln(3))`

`x = (ln((1)/(3)))/(2ln(3))`

`x = (-ln(3))/(2ln(3))`

`x = -(1)/(2)`

Answer 2

If it is log 81 base 1/9=x, then you can make the following equation
(1/9)^x=81
x=-2
in this case since 9 squared is 81 and you need to flip the fraction so you add a negative,
Hope this helps.