How do you solve #log_4 (m + 2) - log_4(m - 5) = log_4 8#?

1 Answer
Apr 28, 2016

Answer:

#m=6#

Explanation:

Given,

#log_4(m+2)-log_4(m-5)=log_4(8)#

We can simplify the left side of the equation using the logarithmic property, #log_color(purple)b(color(red)m/color(blue)n)=log_color(purple)b(color(red)m)-log_color(purple)b(color(blue)n)#.

#log_4((m+2)/(m-5))=log_4(8)#

Since the equation now follows a "#log=log#" situation where the bases are the same on both sides, rewrite the equation without the "#log#" portion.

#(m+2)/(m-5)=8#

Solve for #m#.

#m+2=8(m-5)#

#m+2=8m-40#

#7m=42#

#color(green)(|bar(ul(color(white)(a/a)m=6color(white)(a/a)|)))#