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Find the value of log₁₀(1/40) given that log₁₀4 = 0.60217

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Find the value of log₁₀(1/40) given that log₁₀4 = 0.60217

A. 1.6021

B. 1.3979

C. 2.3979

D. -1.6021

QUICK ANSWER…

D

DETAILS…

We have been given all we need to do the calculation…

log₁₀(1/40)

= log₁₀40¯¹

= – 1log₁₀40

= – 1(log₁₀4 × 10)

= – 1(log₁₀4 + log₁₀10)

But log₁₀10 = 1, hence, we have:

= – 1(log₁₀4 + 1)

Recall we were given log₁₀4 as 0.60217

= – 1(0.60217+ 1)

= – 1(1.60217)

= – 1.60217

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is not correct.
  4. D is the correct answer.

KEY-POINTS…

You may please note these/this:

  • If you have access to a calculator, you can quickly do the log of 1/40.
  • In the absence of a calculator, you can quickly apply about three laws of logarithm as done above to arrive at the right answer.
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/ culled from 2020 JAMB-UTME mathematics past question 25 /

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