Question

Log*subscript*(3x − 2) 4096 = 3

I got x= negative 6 is this correct??

Answer 1

remember


`log_a(b)=c` translates to
`a^c=b`
and

`log_a(b^c)=clog_a(b)`
so


4096=16^3

`log_(3x-2)(4096)=3`

`log_(3x-2)(16^3)=3`

`3log_(3x-2)(16)=3`
divide both sides by 3

`log_(3x-2)(16)=1`
translate

`(3x-2)^1=16`
3x-2=16
add 2 to both sides
3x=18
divide both sides by 3
x=6