Log help

Question

0

619

1

Find log_x: \(x=\frac{\sqrt{10 \sqrt{10a}}}{0.1}\)

Guest Feb 4, 2018

CPhill · Answer 1 · 2018-02-05T12:59:59

√[ 10 √(10a )] = 10^(1/2) * (10a)^(1/4) = 10^(1/2 + 1/4) * a*(1/4) =

10^(3/4) * a^(1/4)

So we have

10^(3/4) * a^(1/4) / 0.1 =

10^(3/4) * a^(1/4) / (1/10) =

10 * 10^(3/4) * a^(1/4) =

10^(7/ 4) * a^(1/4)

So

log [10^(7/ 4) * a^(1/4) ] =

log [ 10^(7/4) ] + log a ^(1/4) =

(7/4) log 10 + (1/4) log a =

(7/4) + log a / 4 =

[ 7 + log a ] / 4