Q. 6 E5.0( 1 Vote )

# Simplify the following.

5log_{10}2 + 2log_{10}3 - 6log_{64}4

Answer :

5log_{10}2 + 2log_{10}3 - 6log_{64}4

Here log_{64}4 = x

⇒ 64^{x} = 4

⇒ (4^{3})^{x} = 4

⇒ 3x = 1

⇒

∴

∴ 5log_{10}2 + 2log_{10}3 - 6log_{64}4 = log_{10}2^{5} + log_{10}3^{2} - 2

= log_{10}32 + log_{10}9 - 2log_{10}10

= log_{10}32 + log_{10}9 - log_{10}10^{2}

^{=}

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