Question

expand the following log(200)​

Answer 1

SOLUTION

TO DETERMINE

To expand

$\sf{ log(200) }$

EVALUATION

$\sf{ log(200) }$

$\sf{ = log_{10}(200) }$

$\sf{ = log_{10}(2 \times 100) }$

$\sf{ = log_{10}(2 ) + log_{10}( 100) }$

$\sf{ = log_{10}(2 ) + log_{10}( {10}^{2} ) }$

$\sf{ = log_{10}(2 ) + 2log_{10}(10 ) }$

$\sf{ = log_{10}(2 ) + 2 \times 1 }$

$\sf{ = log_{10}(2 ) + 2 }$

$\sf{ = log(2) + 2 }$

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Answer 2

✫ Question Given :

• expand the following log(200) ?

✫ Required Solution :

✩ Value Given to us :

• ➤ log(200)

✩ According to Question :

• ➤ log10 ( 200 )

• ➤ log10 ( 2 × 100 )

✩ We can write 200 as [ 2 × 100 ]

• ➤ log10 (2) + log10 (100)

• ➤ log10 (2) + log10 (10²)

✩ we can write 100 as [ 10² ]

• ➤ log10(2) + 2log10(10)

• ➤ log10(2) + 2log10

✩ we know log10 = 1

• ➤ log10(2) + 2 × 1

• ➤ log10(2) + 2

✫ Therefore :

➤ Expanded Form log(200) is log(2) + 2

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