Homework SourseGroup Problem 5 ay rithm If a 0 and a 1 then ylog x means
Group Problem 5 ay : rithm: If a > 0 and a 1, then y-log, x means x Definition of k for everyx> 0 and every real numbery 1) Write an example that illustrates that log,( +y) log, r+ log,y. 2) Write an example that illustrates that (log rlog,a . 3) Does 3 )--5? Why or why not? MacBook Pro 
Solution
log 2 ( x+ y) is not equal to log 2 x + log 2 y
lets take an example
log 2 ( 1 + 3 ) = log 2 ( 4) = log 4 / log 2 which is equal to 2
if we write
log 2 ( 1 + 3 ) = log 2 (1) + log 2 (3)
this becomes 1.5849
which is not equal to 2
hence, log 2 ( x+ y) is not equal to log 2 x + log 2 y
2) (log a x)^r
lets take an example
(log 2 4)^3
= (log 4 / log 2 )^3
= 8
now if we write
(log 2 4)^3 = 3 (log 2 4)
this will be equal to 6
hence, we can conclude
(log a x)^r is not equal to r (log a x)
3) 3 ^ log 3 (-5)
log 3 (-5) = log -5 / log 3
3^( log -5 / log 3 )
since log -5 is undefined
hence, 3 ^ log 3 (-5) is undefined
