Question

1/(5800*10 to the power 8)
solve by log

Answer 1

[tex]x = \frac{1}{5800*10^8} \\ \\Log_{10}\ x =\ Log_{10} (\frac{1}{5800*10^8}) = - Log_{10}\ 58*10^{10} \\ \\= - ( Log_{10}\ 58 + Log_{10}\ 10^{10}) =- Log_{10}\ (2\ *\ 3^3) - (10) \\ \\= - (Log_{10} 2 + Log_{10}\ 3^3) - 10 = - (Log_{10}\ 2 + 3\ Log_{10}\ 3) - 10 \\ \\ = -0.30103 - 3* 0.47712 - 10 = - 11.73239 \\ \\x = 10^{-11.73239} = 1.8518 * 10^{-12} = 0.0000000000018518 \\ [/tex]