Q. 9 D5.0( 1 Vote )

# Prove the following equations.

log_{10}0.16 = 2log_{10}4 – 2

Answer :

Let us consider the RHS:

i.e. 2log_{10}4 - 2 = 2log_{10}4 - 2log_{10}10

= log_{10}4^{2} - log_{10}10^{2}

(∵ log_{a}M^{n} = nlog_{a}M)

=

(∵ log_{a}(M ÷ N) = (log_{a}M) - (log_{a}N))

= log_{10}(0.16) = log_{10}0.16

Hence LHS = RHS

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