Question

If log10 2 = 0.3010; log10 3 = 0.4771 and log10 7 = 0.8451 then find log10 105?​

Answer 1

Answer:

given, If log10 2 = 0.3010; log10 3 = 0.4771 and log10 7 = 0.8451.

we have to find value of log10 105.

we know, log_a(xyz)=log_ax+log_ay+log_azlog

a

(xyz)=log

a

x+log

a

y+log

a

z

so, log10 (105) = log10 (3 × 5 × 7)

= log10 3 + log10 5 + log10 7

now putting value of

log10 3 = 0.4771

log10 7 = 0.8451

log10 5 = ? so, we can write log10 5 = log10 (10/2)

[ formula, log_a(x/y)=log_ax-log_aylog

a

(x/y)=log

a

x−log

a

y

so, log10 5 = log10 (10) - log10 2

= 1 - log10 2 [ we know, log10 10 = 1]

= 1 - 0.3010

= 0.6990

now, log10 105 = 0.4771 + 0.6990 + 0.8451

= 2.0212