Question
Solve the following logarithmic equation. Exact words only:
log 3(x+4) = 2+log3(x-20)
the 3 in the part of log (3)should be lower just didn't know how to type it in here
log 3(x+4) = 2+log3(x-20)
the 3 in the part of log (3)should be lower just didn't know how to type it in here
Answers
Reiny
log3 (x+4) - log3 (x-20) = 2 , where clearly x > 20
log3 ( (x+4)/(x-20) ) = 2
(x+4)/(x-20) = 3^2 = 9
9x - 180 = x+4
8x = 184
x = 23
check:
LS = log3 27 = 3
RS = 2 + log3 3
= 2 + 1 = 3 = LS
log3 ( (x+4)/(x-20) ) = 2
(x+4)/(x-20) = 3^2 = 9
9x - 180 = x+4
8x = 184
x = 23
check:
LS = log3 27 = 3
RS = 2 + log3 3
= 2 + 1 = 3 = LS