Question

How do you solve `log_4 8 - log_4(x+6)=1`?

Answer 1

`log_color(magenta)4 color(red)8-log_color(magenta)4 color(blue)((x+6))=1`

Condense the log by using the log property `logcolor(red)a -logcolor(blue)b =log (color(red)a/color(blue)b)`

`log_color(magenta)4 (color(red)8/color(blue)(x+6))=1`

Next, turn the log into an exponential by the rule

`log_color(magenta)b color(orange)x=color(limegreen)a` becomes `color(magenta)b^color(limegreen)a= color(orange)x`.

`log_color(magenta)4 color(orange)((8/(x+6))color(red)=color(limegreen)1`

`color(magenta)4^color(limegreen)1=color(orange)(8/(x+6))`

`4=8/(x+6)`

`4(x+6)=8`

`4x+24=8`

`(4x)/4=-16/4`

`x=-4`