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Mathematics

Evaluate the following:

2log105 + log108 - 12\dfrac{1}{2}log104

Logarithms

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Answer

Given,

⇒ 2log105 + log108 - 12\dfrac{1}{2}log104

⇒ log1052 + log108 - log10412\text{log}_{10}4^{\dfrac{1}{2}}

⇒ log1025 + log108 - log102

⇒ log1025×82\dfrac{25 \times 8}{2}

⇒ log10100

⇒ log10102

⇒ 2log1010

⇒ 2.

Hence, 2log105 + log108 - 12\dfrac{1}{2}log104 = 2.

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