Question

express as a single logarithms
2+1/2 log 10 9 - 2 log 10 5
​

Answer 1

Answer:

Step-by-step explanation: given below in image

Answer 2

$\underline{ \underline{ {\huge{\mathtt{A}}} \sf NSWER - }}$

$▪ \: \sf \: 2 + \dfrac{1}{2} log_{10}(9) - 2 log_{10}(5)$

Now,

we know that,

$\blue{\sf : \implies log_{10}(100) = 2 }\\ \blue{ \sf : \implies log(9) = log( {3}^{2} ) }\\ \blue{ \sf : \implies2 log(5) = log( {5}^{2} ) }$

$\sf \therefore \: log_{10}(100) + log_{10}( {9}^{ \frac{1}{2} } ) - log_{10}( {5}^{2} ) \\ \sf \: = \: log_{10}(100) + log_{10}( {3}^{ \cancel2 \times \frac{1}{ \cancel2} } ) - log_{10}(25) \\ \sf = \: log_{10}(100) + log_{10}(3) - log_{10}(25)$

we know that,

$\blue{ \sf : \implies { log_{a} + log_{b} - log_{c} = log( \frac{a \times b}{c} ) }}$

$\sf \therefore \: log_{10}( \frac{100 \times 3}{25} ) \\ \\ \sf = \: log_{10}( \frac{ \cancel{100} \: ^{4} \times 3}{ \cancel{25}} ) \\ \\ \boxed{ \red{ \sf = \: log_{10}(12) \: \: \: \: \: \: \: ans...}}$

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