Question

show that 3log4-4log5+3log25-2log15=log64/9​

Answer 1

Answer:2 log 15/18 - log 25/162 + log 4/9

= 2 log 15 - 2 log 18 - log 25 + log 162 + log 4 - log 9

= 2 log 3*5 - 2 log 2*32 - log 52 + log 2*34 + log 22 - log 32

= 2 log 3 + 2 log 5 - 2 log 2 - 2 log 32 - log 52 + log 2 + log 34 + log 22 - log 32

= 2 log 3 + 2 log 5 - 2 log 2 - 2*2 log 3 - 2 log 5 + log 2 + 4 log 3 + 2 log 2 - 2 log 3

= 2 log 3 + 2 log 5 - 2 log 2 - 4 log 3 - 2 log 5 + log 2 + 4 log 3 + 2 log 2 - 2 log 3

= 2 log 3 - 2 log 3 + 4 log 3 - 4 log 3 +2 log 5 - 2 log 5 - 2 log 2 + log 2 + 2 log 2   //rearranging the like terms

= log 2  //cross out whichever cancel each other

Step-by-step explanation: