If log 4.17=.6201, how can I use that to find log 417 and log .417?

Answer 1

if these are decimal logarithms, i.e. log base 10, use the formula

log(ab) = log a + log b

for example,

log(417) = log (4.17 * 100) = log 4.17 +log100
= .6201 + 2
=2.6201

log0.417 = log 4.17 + log0.1 = .6201 -1 = -0.3799

log(.1) = log (10^(-1)) = -1

Answer 2

log(417) =
log(4.17 * 10^2) =
log(4.17) + log(10^2) =
.6201 + 2 =
2.6201

log(.417) =
log(4.17/10) =
log(4.17) - log(10) =
.6201 - 1 =
-.3799

So there you go.

Keep in mind log(x/y) = log(x) - log(y) an log(xy) = log(x) + log(y)

Answer 3

log(417) =
log (4.17 x 10^2) =
log(4.17)+log(10^2) =
0.6201 + 2 = 2.6201

Similar for log(.417) except it's log(4.17 x 10^-1)