Question

Given that log 8 = 0.9031 and log 9 = 0.9542. Find out the value of log 120 correct to four decimal places.​

Answer 1

$\bold{\green{\underline{Question :}}}$

Given that log 8 = 0.9031 and log 9 = 0.9542. Find out the value of log 120 correct to four decimal places.

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Given,

• log 8 = 0.9031
• log 9 = 0.9542

Since, the values are directly given, we have to utilise it to find thevvue of log 120.

As per theory of logarithms, we know :

10¹ = 10 ∴ Log 10 to base 10 = 1

or simply log 10 = 1

• log 8 = 0.9031 (given)

∴ log 8 = log(2)³ = 3 × log 2 = 0.9031

∴ log 2 = 0.9031/3 = 0.30103

∴ log 2 = 0.30103

• log 9 = 0.9542 (given)

∴ log 9 = log(3)² = 2 × log 3 = 0.9542

∴ log 3 = 0.9542/2 = 0.4771

∴ log 3 = 0.4771

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Now we are ready with the flowing values,

log 3 = 0.4771 ; log 2 = 0.30103 ; log 10 = 1

∴ log 120 = log (3 × 4 × 10)

⇝ log (3 × 2 × 2 × 10)

⇝ log 3 + log 2 + log 2 + log 10

Applying the values, we get,

⇝ 0.4771 + 0.30103 + 0.30103 + 1

⇝ 2.07916

⇝ say 2.0792 (four decimal places).

∴ log 120 = 2.0792.

Answer 2

Answer:

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