natural logarithm?

Question

Question
d=.043
scientific notaion=4.3x10^-2
log=4.3e^-2????????

Answer 1

> log=4.3e^-2????????

No.

If you use COMMON logarithms (base 10) then:

log(d)
= log(4.3 × 10^-2)
= log(4.3) + log(10^-2) [because log(ab) = log(a)+log(b)
= log(4.3) + (-2)log(10) [because log(a^b) = b(log(a))]
= log(4.3) + (-2)(1) [because the COMMON log of 10 is 1.]

So, the common log of 4.3×10^-2 is log(4.3)−2

If you use NATURAL logarithms, you get:

ln(d)
= ln(4.3 × 10^-2)
= ln(4.3) + ln(10^-2)
= ln(4.3) + (-2)ln(10)

This really can't be reduced any further (without a calculator).