How do you find #\log _ { 6} ( x + 4) = \log _ { 6} 7#?

1 Answer
Mar 2, 2018

Answer:

The answer is #x=3#.

Explanation:

Use the definition of a logarithm:

#color(white)=>log_color(red)a(color(green)b)=color(blue)xqquad<=>qquadcolor(red)a^color(blue)x=color(green)b#

In this case, #a# is #6#, #b# is #x+4#, and #x# is #log_6(7)#. It sounds kind of confusing, but I'll use colors so it's easier to see:

#color(white)=>log_color(red)6(color(green)(x+4))=color(blue)(log_6(7))#

#=>color(red)6^color(blue)(log_6(7))=color(green)(x+4)#

Now, the #6# and #log_6# cancel out:

#color(white)=>color(red)cancel(color(black)6)^(color(red)cancel(color(black)(log_6))(7))=x+4#

#=>7=x+4#

#color(white)=>3=x#

The answer is #x=3#.