Question

If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5^a+b-c = 1

Answer 1

Consider `"log"(5^("a"+"b"-"c"))`

= (a + b - c)log5 

= `("log"3/5 + "log"5/4 -2"log"sqrt(3/4))"log"5`

= `("log"3/5 + "log"5/4 - "log"[sqrt(3/4)]^2)"log"5`

= `("log"3/5 + "log"5/4 - "log"3/4)"log"5`

= `"log"((3/5 xx 5/4)/(3/4))"log"5`

= log1 x log5 = 0    ...[∵ log1 = 0]
∴ `5^("a"+ "b"-"c")`
= 10°
= 1.