Given that \log_a(5)\approx0.65 and \log_a(3)\approx0.44, evaluate e

Zoe Oneal 2021-11-06 Answered
Given that loga(5)0.65 and loga(3)0.44, evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the logarithms of 5 and 3
a)loga(0.6)
b)loga(3)
c)loga(15)
d)loga(25)
e)loga(75)
f)loga(1.8)
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Expert Answer

jlo2niT
Answered 2021-11-07 Author has 96 answers
Step1
loga(5)0.65loga(3)0.44
properties of logarithms are
1.log(ab)=logc(a)+logc(b)
2.logc(ab)=logc(a)logc(b)
3.logc(ab)=blogca
Step2
loga(0.6)=loga(35)
loga(0.6)=loga(3)loga(5)
loga(0.6)=0.440.65
loga(0.6)=0.21
Step3
loga(3)=loga(312)
loga(3)=12loga(3)
loga(3)=120.44
loga(3)=0.22
Step4
loga(15)=loga(53)
loga(15)=loga(5)+loga(3)
loga(15)=0.65+0.44
loga(15)=1.09
Step5
loga(25)=loga(52)
loga(25)=2loga(5)
loga(25)=20.65
loga(25)=1.3
Step6
loga(75)=loga(253)

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