Question

1. X+10=log3^81. 2. Log9 (2x—8)=4. 3. Log(-2a+9)= log(7–4a)

Answer 1

1.
`x=-6`

2.
`x=(6569)/(2)`

3.
`a=-1`

Explanation:

1.
`x+10=\log _3\left(81\right)`

`x+10-10=\log _3\left(81\right)-10`

`x+10-10`

`= x`

`\log _3\left(81\right)-10`

`\log _3\left(81\right)`

`=\log _3\left(3^4\right)`

`=4\log _3\left(3\right)`

`= 4`

`4-10`

`x=-6`

2.
`\log _9\left(2x-8\right)=4`

`2x-8=9^4`

`2x-8=6561`

`2x-8+8=6561+8`

`2x=6569`

`(2x)/(2)=(6569)/(2)`

`x=(6569)/(2)`

3.
`\log _(10)\left(-2a+9\right)=\log _(10)\left(7-4a\right)`

`-2a+9=7-4a`

`-2a+9-9=7-4a-9`

`-2a=-4a-2`

`-2a+4a=-4a-2+4a`

`2a=-2`

`(2a)/(2)=(-2)/(2)`

`a=-1`