Question

Express as single logarithm: 2 log ( base 10) 5 - log(base 10) 2 + 3 log(base 10) 4 + 1​

Answer 1

Answer:

given, 2 log 5 - log 2 + 3 log 4 + 1

solution: [ m log n = log n^m , 1 = log 10 and

log m + log n - log p = log { (m×n)/p } ]

using the above formulae, we can rewrite the given logarithmic expression as,

=> log 5^2 - log 2 + log 4^3 + log 10

=> log 25 + log 64 + log 10 - log 2

=> log [ (25×64×10)/2 ]

=> log (125×64)

=> log (8000)