[tex] \sf{}Prove \: \: that \: \: \: log_{10} \: \: 2 \: \: lies \: \: between \: \\ \sf{}\: \frac{1}{3} and \: \frac{1}{4} [/tex]
Share
[tex] \sf{}Prove \: \: that \: \: \: log_{10} \: \: 2 \: \: lies \: \: between \: \\ \sf{}\: \frac{1}{3} and \: \frac{1}{4} [/tex]
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Answer:
[tex] \huge \fbox \color{lime}{꧁Solution࿐}[/tex]
️️
To prove:-
[tex] \tt \: \frac{1}{3} < log_{10}(2) < \frac{1}{4} \\ [/tex]
️️
Proof:-
Step1- Simplification of term
[tex] \tt {2}^{12} = 4096[/tex]
=> 1000 < 4096 < 10000
[tex] \tt = > {10}^{3} < {2}^{12} < {10}^{4} [/tex]
️️
Step2- Taking logarithm to the base 10
[tex] \tt{10}^{3} < {2}^{12} < {10}^{4} \\ [/tex]
[tex] \tt log_{10}( {10}^{3} ) < log_{10}( {2}^{12} ) < log_{10}( {10}^{4} ) \\ [/tex]
[tex] \tt = > 3 \: log_{10}(10) < 12 \: log_{10}(2) < 4 \: log_{10}(10) \\ [/tex]
[tex] \tt = > 3 < 12 \: log_{10}(2) < 4 \\ [/tex]
[tex] \tt = > \frac{3}{12} < log_{10}(2) < \frac{4}{12} \\ [/tex]
[tex] \tt \green{= > \frac{1}{3} < log_{10}(2) < \frac{1}{4} }[/tex]
Hence proved
____________________________________
Evergreen forests, orange, tea, coffee, and cardamom plantations enriched with spectacular valleys and misty mountains make Nelliampathy an exotic location. Nelliampathy often called 'Poor man's Ooty' is also famous for the trekking trails and the amazing climate, and nature's magic which enhance the whole experience.
So hot you are looking in your dp!
really!!