Question

find find the value of log 10 to the base 40 log 5 to the base 10 equals to a and log to the base 10 equals to b​

Answer 1

Answer:

given

log 5 to base 10 = a   ,  

so  10 ^ a = 5            

log 3 to base 10 = b

so 10 ^ b = 3

therefore

log 15 to base 40 = log (3 ×5 ) to base 40

                            = log (10 ^ b)( 10 ^ a) to base 40

                            =  log 10^ (a+b)to base 40

                            = (a+b ) log 10 to base 40

                            =  (a+b ) log (2 ×5 )to base 40

                            = (a+b ) log (2 × 10^a ) to base 40

                            = (a+b )  {  log (2 ) to base 40 + log (10^a ) to base 40  }

                           = (a+b )  {  log (2 ) to base 40 + a  log (10 ) to base 40  }