b.The approximation of the natural logarithm of 2: ln 2 ≈ 0.693 is commonly used by applied scientists, biologists, chemists, and computer scientists. For example, chemists use it to compute the half-life of decaying substances. Based on this approximation and the power rule for logarithmic expressions, how could you approximate ln 8, without a calculator? Explain.

Question

y2o2 · Answer

ln(8)  = ln(2^3) = 3ln(2) = 3*0.693 = 2.079

anonymous · Answer

please explain why that is true ^_^

y2o2 · Answer

because of the logarithm rule:

log(a^n)  = nlog(a)

do you want a proof ?!

anonymous · Answer

Thank you! /bow

anonymous · Answer

haha nono i believe you, i just had to say why it was true, but i didnt know what to say rofl

anonymous · Answer

notations log[base]{value} .. from formula we have if value is some power of base then the degree of power then degree is answer for that logarithm . so if base log[2]{25} hten if you know log[2]{5} is x then you can deduce log[2]{25} as => log[2]{5pow(2)}=> 2*log[2]{5}=>2*x; This is the general approach of getting result

anonymous · Answer

excellent answer!