Question

Given that
$log_{10}(2)$
=0.3010 and
$log_{10}(5)$
=0.6990,
evaluate correct to 3 significant figures
$log_{10}(50) - log_{10}(40)$

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Answer 1

Solution :

Given log₁₀2 = 0.3010 , log₁₀5 = 0.6990

Now, log₁₀50 - log₁₀40

  = log₁₀(5² × 2) - log₁₀(2³ × 5)

  = (log₁₀5² + log₁₀2) - (log₁₀2³ + log₁₀5)

  = 2log₁₀5 + log₁₀2 - 3log₁₀2 - log₁₀5

  = log₁₀5 - 2log₁₀2

  = 0.6990 - 2(0.3010)

  = 0.6990 - 0.6020

  = 0.0970

➞ log₁₀50 - log₁₀40 = 0.970 , which is the required value correct to 3 significant figures.