Question

(iii) Prove that : log 125 = 3(1 - log 2).​

Answer 1

Given,

$\sf{log125 = 3(1 - log2)}$

RHS

$\sf{3(1 - log2)} \\ \\ = \sf{3 - 3 log(2) } \\ \\ = \sf{3 log_{10}(10) - 3 log_{10}(2) } \\ \\ = \sf{log(10 {}^{3} ) - log( {2}^{3} ) } \\ \\ = \sf{ log( \frac{ {10}^{3} }{ {2}^{3} } ) } \\ \\ = \sf{ log( {5}^{3} ) } \\ \\ = \tt{ log(125) }$

Hence,Proved

Note

$\tt{log10 = 1} \\ \\ \tt{ log(a) - log(b) = log( \frac{a}{b} ) } \\ \\ \tt{ log(a) + log(b) = log(ab) }$

Answer 2

Answer:

Step-by-step explanation: