How to simplify logarithm?
Can anyone please explain to me how to do question d, when there I see different bases? Thanks!
Can anyone please explain to me how to do question d, when there I see different bases? Thanks!
1 Answer
Sep 23, 2017
Explanation:
"there are 2 possible approaches"
(1)color(blue)" Evaluation"
•color(white)(x)log_b x=nhArrx=b^n
rArrlog_4 32=nrArr32=4^n
"express the equation in base 2"
rArr2^5=(2)^(2n)
"equating the exponents"
2n=5rArrn=5/2color(red)(larr)
"similarly for "log_9 27=n
rArr27=9^n
"expressing the equation in base 3"
3^3=3^(2n)
rArr2n=3rArrn=3/2color(red)(larr)
rArrlog_4 32-log_9 27=5/2-3/2=1
(2)color(blue)" Change of base"
•color(white)(x)log_b a=log_c a/log_c b
"choose base 10 as this can be evaluated on calculator"
rArrlog_4 32-log_9 27
=log_10 32/log_10 4-log_10 27/log_10 9
=2.5-1.5=1