Question

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

Answer 1

`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)|)))`