Question

How do you simplify `\log _{3}8+\log _{3}7+\log _{3}11`?

Answer 1

The expression is equivalent to `log_3 616` which is about `5.84669...`

Explanation:

You can simplify this because it's just a bunch of numbers, so you can condense it using this logarithm rule:

`log_color(green)acolor(red)x+log_color(green)acolor(blue)y=log_color(green)a(color(red)xcolor(blue)y)`

Here's our expression:

`color(white)=log_3 8+log_3 7+log_3 11`

`=log_color(magenta)3 color(red)8+log_color(magenta)3 color(blue)7+log_color(magenta)3 color(green)11`

`=log_color(magenta)3 (color(red)8*color(blue)7*color(green)11)`

`=log_color(magenta)3 (color(purple)56*color(green)11)`

`=log_color(magenta)3 (color(brown)616)`

`~~5.84669...`

Answer 2

`log_3 616`

Explanation:

`"using the "color(blue)"law of logarithns"`

`•color(white)(x)logx+logy=log(xy);x,y>0`

`"this can be extended to more than 2 terms"`

`rArrlog_3 8+log_3 7+log_3 11`

`=log_3(8xx7xx11)=log_3 616`