Question

Calculate log 10(1/216) to 3 decimal places.
Given log 6 = 0.778​

Answer 1

Answer:

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Answer 2

Given:

$\log 10(\dfrac{1}{216} )$ and  $\log 6$ = 0.778​

We have to find, the value of $\log 10(\dfrac{1}{216} )$ = ?

Solution:

∴ $\log 10(\dfrac{1}{216} )$

Using the logarithm identity,

$\log ab=\log a+ \log b$

= $\log 10+\log (\dfrac{1}{216} )$

[∵ 216 = 6 × 6 × 6 = $6^{3}$]

= $\log 10+\log (\dfrac{1}{6^3} )$

= $\log 10+\log 6^{-3}$

Using the logarithm identity,

$\log a^{b}=b\log a$ and $\log 10$ = 1

= 1 $-3\log 6$

Put $\log 6$ = 0.778​, we get

= 1 - 3 × 0.778

= 1 - 2.334

= - 1.334

∴ The value of $\log 10(\dfrac{1}{216} )$ = - 1.334