How do you condense #Log_4 (20) - Log_4 (45) + log_4 (144)#?
2 Answers
Explanation:
#"using the "color(blue)"laws of logarithms"#
#•color(white)(x)logx+logy=log(xy)#
#•color(white)(x)logx-logy=log(x/y)#
#•color(white)(x)log_b x=nhArrx=b^n#
#log_4 20+log_4 144-log_4 45#
#=log_4((20xx144)/45)#
#=log_4(64)=n#
#64=4^3=4^nrArrn=3#
Explanation:
The log product and quotient rules allow us to combine these terms, as long as the logs have the same base:
All the terms in this problem have logs of base 4, so we can apply these rules:
Of course, the result of a log is the exponent of the base that will give you that number:
So, since