Question

log4(x-4)+log4(x+59)=3

Answer 1

\(\Large\color{black}{ \displaystyle \log_\color{red}{\rm a}\left( \color{blue}{\rm b} \right)+\log_\color{red}{\rm a}\left( \color{blue}{\rm d} \right)=\log_\color{red}{\rm a}\left( \color{blue}{\rm b \times d } \right) }\)

Answer 2

use that for your left side.

Answer 3

\(\large\color{black}{ \displaystyle \log_\color{red}{\rm 4}\left( \color{blue}{\rm x-4} \right)+\log_\color{red}{\rm 4}\left( \color{blue}{\rm x+59} \right)=\log_\color{red}{\rm a}\left( \color{blue}{\rm ~~~(x-4)\times (x+59)~~~} \right) }\)

Answer 4

the last "a" on the right should be 4

Answer 5

\(\large\color{black}{ \displaystyle \log_\color{red}{\rm 4}\left( \color{blue}{\rm ~~~(x-4)\times (x+59)~~~} \right)=3 }\)

\(\large\color{black}{ \displaystyle \log_\color{red}{\rm 4}\left( \color{blue}{\rm ~~x^2-4x+59x-236~~} \right)=3 }\)

\(\large\color{black}{ \displaystyle \log_\color{red}{\rm 4}\left( \color{blue}{\rm ~~x^2+55x-236~~} \right)=3 }\)

\(\large\color{black}{ \displaystyle x^2+55x-236=4^3 }\)

\(\large\color{black}{ \displaystyle x^2+55x-236=64 }\)

\(\large\color{black}{ \displaystyle x^2+55x-300=0 }\)

Answer 6

would i do the quadratic formula next?

Answer 7

factor it

Answer 8

60 - 5 = 55
60 * (-5) = -300

Answer 9

(x+60)(x-5)= -60,5