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

1 Answer
Oct 20, 2016

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