Question

Find the value
of log√2 base 7 if log
2 = .3010 and log7 =
.4950​

Answer 1

Answer:

0.3040

Step-by-step explanation:

log 10 (2) = 0.3010

log 10 (7) = 0.4950

log 7 (_/2)

[ log a (b) = log 10 (b) / log 10 (a) ]

log 7 (_/2) = log 10 ( 2^0.5) / log 10 (7)

[ log a (b^x) = x log a (b) ]

log 7 (_/2) = 0.5 log 10 (2) / log 10 (7)

= 0.5 × 0.3010 / 0.4950

= 0.3040