Question

How do you solve `\log _ { 3} ( \frac { 1} { 9} ) = x`?

Answer 1

here `x=-2`

Explanation:

`log_3(1/9)=x` can be written as`log_3(9^-1)=xrArrlog_3(3^-2)=xrArr-2(log_3(3))=x`
`rArrx=-2` the properties I used are :
`log(1/x)=-logx,log_aa=1,log_aa^2=2log_aa`

Answer 2

`x=-2`

Explanation:

`"using the "color(blue)"law of logarithms"`

`•color(white)(x)log_bx=nhArrx=b^n`

`log_3(1/9)=x`

`rArr1/9=3^x`

`"note that "1/9=3^-2=3^x`

`rArrx=-2`