Question

2log2+ log5 -1/2 log 36 - log 1/30

Answer 1

Answer: 2

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Step-by-step explanation:

2log2+ log5 -1/2 log 36 - log 1/30

= 2 log 2 + log 5 -1/2 log 6^2 - log (30 )^-1

= 2 log 2 + log 5 -1/2 *2 log 6 + log 30   ----> log x ^ y = y log x

= 2 log 2 + log 5 - log 6  + log (6*5)

= 2 log 2 + log 5 - log 6 + log 6 + log 5------> log xy = log x +log y

=2 log 2 + log 5 + log 5

=2 log 2 +2 log 5

= log 2^2 + log 5^2  -------> log x ^ y = y log x

= log 4 + log 25

= log (4*25)

= log 100

= log 10^2 --=----> log ₁₀ 10 =1

= 2