Question

Evaluate : 2 log 2+log 5-1/2 log 36-log 1/30

Answer 1

2log2+log5-1/2log36-log1/30
=log4+log5-log6+log30
=log(5×4×30÷6)
=log(100)
=2

Answer 2

Answer:

Required value is 2

Step-by-step explanation:

Given,

$2 log(2) + log(5) - \frac{1}{2} log(36) - log( \frac{1}{30} )$

$log( {2}^{2} ) + log(5) - log( {36}^{ \frac{1}{2} } ) - log( \frac{1}{30} )$

$= log(4) + log(5) - log( \sqrt{36} ) - ( log(1) - log(30) )$

$= log(4) + log(5) - log(6) - (0 - log(30) )$

$= log(4) + log(5) - log(6) + log(30)$

$= log(4) + log(5) + log(30) - log(6) \\ = log(4) + log(5) + log( \frac{30}{6} ) \\ = log(4) + log(5) + log(5) \\ = log(( 4\times 5 \times 5)) \\ = log(100) \\ = log( {10}^{2} ) \\ = 2 log(10) \\ = 2 \times 1 \\ = 2$

Here applied formulas are

$log(1) = 0 \\ log(x) + log(y) = log(xy) \\ log(x) - log(y) = log( \frac{x}{y} ) \\ log( \frac{1}{x} ) = - log(x) \\ log_{10}(10) = 1 \\ log( {x}^{y} ) = y log(x)$

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