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Well I've tried equating to $x$ i.e. $$3^x =0.095,$$

then taking both side to $\log_{10}$, so we have $$\log_{10}3^x =\log_{10}0.095$$, then I crossed $x$ to the other side ,i.e., $$x\log_{10}3=\log_{10}0.095.$$

Then I divided both sides by $\log_{10}3$.

Meaning that $$x =\frac{\log_{10} 0.095}{ \log_{10}3}$$

Then i solved on but didn't get the answer and I was confused, our head of study group says the answer is $-2.14$. Guys help , pls its not a homework

Siong Thye Goh
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Emeka Okolie
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1 Answers1

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$$x=\frac{\log_{10}0.095}{\log_{10} 3} \approx -2.14$$

Perhaps you have trouble reading the table?

Just a simple check: $$log_{10}(0.095) \approx -1.022$$

Do you get that?

Siong Thye Goh
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  • Yeah you edited it right. Pls i meant solving without a calculator and pls break log 10^0.095 down may explain further – Emeka Okolie Oct 14 '16 at 21:28
  • Do you have the table that you are using online? Just want to make sure we are looking at the same table. – Siong Thye Goh Oct 14 '16 at 21:34
  • http://myhandbook.info/table_commonlog.html Suppose you are using this table. you can find the value of $\log_{10}(9.5)$ there. So use the trick $\log_{10} (0.095)=\log_{10} (9.5 \times 10^{-2})=-2+\log_{10}(9.5).$ – Siong Thye Goh Oct 14 '16 at 21:42
  • p/s: typing tips, include "dollar sign" around mathy stuff. for subscript use "_". Type log as "\log". – Siong Thye Goh Oct 14 '16 at 21:44