Question

prove that 7log16/15+5log25/54+3log87/80=log2

Answer 1

7 Log  16/15  + 5  Log  25 /54  +  3  Log  87/80  
= 7 Log  16 - 7 Log 15 + 5 log 25 - 5 Log 54 + 3 Log 87 - 3 log  80
= 7 * Log 2⁴ - 7 Log (3 * 5)  + 5 Log 5² - 5 Log (2*3³) + 3 Log (29*3) - 3 Log (2⁴*5)
= 28 Log 2 - 7 Log 3 - 7 Log 5 + 10 Log 5 - 5 Log 2 - 15 Log 3 + 3 Log 29 + 3 Log 3 - 12 Log 2 - 3 Log 5

= 11 Log 2 - 19 Log 3 =  Log (2¹¹ / 3¹⁹)

the answer is not  Log 2.

There is something not right in the given question.