Question

prove that log10 2 lies between 1/3 and 1/4​

Answer 1

Answer:

$\frac{1}{4} < log_{10}(2) < \frac{1}{3}$

Step-by-step explanation:

think,

log10 2= a

${10}^{a} = 2$

lcm of 3 and 4 is 12.

${10}^{12a} = {2}^{12} = 4098$

we know that,

$1000 < 4098 < 10000 \\ = {10}^{3} < {10}^{12a} < {10}^{4} \\ = 3 < 12a < 4 \\ = \frac{1}{4} < a < \frac{1}{3} \\ = \frac{1}{4} < log_{10}(2) < \frac{1}{3}$

Proved