SOLUTION: 5. (8 pts) (a) log3 1 =_______ (fill in the blank) (b) Let 𝑥 = log3 1/243 State the exponential form of the equation. (c) Determine the numerical value of log3 1/243 , in si

Algebra ->  Equations -> SOLUTION: 5. (8 pts) (a) log3 1 =_______ (fill in the blank) (b) Let 𝑥 = log3 1/243 State the exponential form of the equation. (c) Determine the numerical value of log3 1/243 , in si      Log On


   

Question 1135953: 5. (8 pts)
(a) log3 1 =_______ (fill in the blank)
(b) Let 𝑥 = log3 1/243 State the exponential form of the equation.
(c) Determine the numerical value of log3 1/243 , in simplest form. Work optional
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
log%283+%2C%281%29%29 =___0____ (fill in the blank) because3%5E0=1

(b) Let x+=+log%283%2C+%281%2F243%29%29+ State the exponential form of the equation.
+y+=+log%28b%2C+x%29 is equivalent to b%5E+y+=+x
in your case 3%5Ex=1%2F243

(c) Determine the numerical value of log%283%2C+%281%2F243%29%29 , in simplest form
log%283%2C+1%2F243%29
=log%28%281%2F243%29%29%2Flog%283%29
=%28log%281%29-log%28243%29%29%2Flog%283%29
=-log%283%5E5%29%2Flog%283%29=
=-5log%283%29%2Flog%283%29
=-5

answer:=>log%283%2C+%281%2F243%29%29=-5

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
3^0=1, so the answer is 0.
1/243 is 3^(-5); 3^x=1/243, so x=-5
log 3 (1/243)=-5
it is also log 3 (1)- log (3) 243), which is 0-5 or -5.