If log10 2 0 3010 and log10 3 0 4771 then the value of log100 0 72 is equal to ........

Quantitative Aptitude (CDS) Simplification

If log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4771, then the value of log₁₀₀ (0.72) is equal to

0.9286

$\bar1.9286$

1.8572

$\bar1.8572$

log₁₀₀(0.72) = log(0.72) / log(100)

$=\frac{log(72/100)}{log 100}$

$=\frac{log(72)- log(100)}{log 100}$

$=\frac{log(2^{3} \times 3^{2})-log10^{2}} {log10^{2}}$

$=\frac{3log2+2log3 -2 } {2log10}= \frac{0.903+0.9542-2}{2}$

$=\frac{-0.1428}{2}= -0.0714= \bar1.9286$

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