Question

How do you condense `log_5 (240) − log_5 (75) − log_5 (80)`?

Answer 1

`log_5 240 - log_5 75 -log_5 80` `=log _5(1/25)`->`=-2`

Explanation:

`log_5 240 - log_5 75 -log_5 80`
`=log_5(240/(75*80))`
`=log _5(1/25)`
`=log_5(1/5^2)`
`=log_5 5^-2`->Use property `1/x^n = x^-n`
`=-2* log_5 5`->use property `log_bx ^n=n*log_b x`
`=-2*1`->use property `log_b b=1`
`=-2`