Question

if log 10 8=0.90; find the value of log 0.125

Answer 1

$Given \: log_{10} 8 = 0.90 \: --(1)$

$Value \: of \: log 0.125 \\= log \frac{125}{1000} \\= \log \frac{125}{125 \times 8}\\= log \frac{1}{8} \\= log 8^{-1} \\= -1 \times log_{10} 8$

$\boxed { \pink { Since, log a^{m} = m log a }}$

$= -1 \times 0.90 \: [ From \: (1) ]$

$= - 0.90$

Therefore.,

$\red{Value \: of \: log 0.125}\green {= -0.90 }$

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