Question

Question #0c8b4

Answer 1

The application of the properties of logarithms is needed here to solve for the value of x.

`log a - log b = log (a/b)`
This is a common logarithm. Therefore, the base is 10

Applying this property,

`log 3(x) - log 3(x+6) = -1`

`log[ (3x)/(3(x+6)]] = -1`

then applying log b = y, which is `10^y = b`

Therefore,

`[(3x)/(3(x+6))] = 10^-1`

take note,`a^-1= (1/a)`

Simplifying,
`(3x)/(3x+18) = 1/10`

then we cross multiply

`10*3x = 1* (3x+18)`
`30x = 3x +18`

add -3x to both sides

`30x -3x = 3x +( -3x) +18`

then,

`27x = 18`

divide by 27

`x= (18/27)`

reducing to lowest term

`x= 2/3`

we are asked to round off to two decimals. Therefore the answer is `0.67`