Question

How do you solve `log_9 4+2 log_9 5=log_9 w`?

Answer 1

`w=100`

Explanation:

`1`. Use the log property, `log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)`, to rewrite `2log_(9)5`.

`log_(9)4+2log_(9)5=log_(9)w`

`log_(9)4+log_(9)5^2=log_(9)w`

`2`. Use the log 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)` to simplify the left side of the equation.

`log_(9)(4*5^2)=log_(9)w`

`log_(9)(100)=log_(9)w`

`3`. 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.

`100=w`

`color(green)(|bar(ul(color(white)(a/a)w=100color(white)(a/a)|)))`