Question

How do you solve `log_5 9 - log_5 (x-5)=log_5 45`?

Answer 1

`x=26/5`

Explanation:

Using the `color(blue)"laws of logarithms"`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(logx-logy=log(x/y))color(white)(a/a)|)))........ (A)`
Applies to logarithms to any base.

`color(red)(|bar(ul(color(white)(a/a)color(black)(log_b x=log_b yrArrx=y)color(white)(a/a)|)))........ (B)`

Using (A)

`log_5 9-log_5(x-5)=log_5(9/(x-5))`

Using (B)

`log_5(9/(x-5))=log_5 45rArr9/(x-5)=45`

solve `45(x-5)=9rArrx=26/5`