Math, asked by divyanshu5941, 1 year ago

If \log_{10}3=0.4771212, without using log tales, find \log_{10}9, \ \log_{10}\sqrt{3}, \ \log_{10}\frac{1}{9} \ and \ \log_{10}(0.3).

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Answered by Nobody12345
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Answered by 23saurabhkumar
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Answer:

(i) log_{10}9=0.954

(ii) log_{10}\sqrt{3}=0.2385

(iii) log_{10}\frac{1}{9}=-0.954

(iv) log_{10}0.3=-0.523

Step-by-step explanation:

In the given question,

We have the value given to us of the term,

log_{10}3=0.4771212

So, we have to find the value of the other terms from the given term's value.

Now, from the properties of the logarithms we have,

loga^{n}=nloga\\and,\\log\frac{a}{b}=loga-logb

So, doing the same we get,

i) log_{10}9=log_{10}(3)^{2}=2log_{10}3=2\times 0.4771212=0.954

Therefore,

log_{10}9=0.954

ii) log_{10}\sqrt{3}=\frac{1}{2}log_{10}3=\frac{1}{2}(0.4771212)=0.2385

Therefore,

log_{10}\sqrt{3}=0.2385

iii) log_{10}\frac{1}{9}=log_{10}1-log_{10}(9)=-log_{10}9=-0.954

Therefore,

log_{10}\frac{1}{9}=-0.954

iv) log_{10}0.3=log_{10}\frac{3}{10}=log_{10}3-log_{10}10=log_{10}3-1=0.477-1=-0.523

Therefore,

log_{10}0.3=-0.523

Therefore,

We have all the values of the required terms as 0.954, 0.2385, -0.954 and -0.523 respectively.

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