Question

How do you simplify `log_3 27 + 6log_3 9`?

Answer 1

`log_3 27 + 6 log_3 9 = color(green)(15)`

Explanation:

Always remember when dealing with log functions
`color(white)("XXX")log_b a = c hArr b^c=a`

So
`color(white)("XXX")color(red)(log_3 27= c_1)`
`color(white)("XXXXXX")`means `3^(c_1)=27 rarr color(red)(c_1=3)`
and
`color(white)("XXX")color(blue)(log_3 9 = c_2)`
`color(white)("XXXXXX")`means `3^(c_2) = 9 rarr color(blue)(c_2=2)`

Therefore
`color(white)("XXX")color(red)(log_3 27) + 6 color(blue)(log_3 9)`
`color(white)("XXX")=color(red)(3)+6*color(blue)(2)`
`color(white)("XXX")=15`