log25+log2xlog50+(log2)^2=?

Hello Guest!

log25+log2xlog50+(log2)^2=?

log25 + log2 x log50 + (log2)²

    = 1,39794000867 + 0,301029995664 x 1,69897000434

       + 0,301029995664²

    = 2

log25 + log2 x log50 + (log2)² = 2

Greeting asinus :- )

  !

log25+log2xlog50+(log2)^2=?

\(\small{ \begin{array}{rcll} && \log(25)+ \log(2) \cdot \log(50)+[\log(2)]^2 \\ &=& \log(5^2)+ \log(2) \cdot \log(2\cdot 5^2)+ \log(2)\cdot \log(2) \\ &=& 2\cdot\log(5)+ \log(2) \cdot [~ \log(2) +\log(5^2) ~]+ \log(2)\cdot \log(2) \\ &=& 2\cdot\log(5)+ \log(2) \cdot \log(2) + \log(2)\cdot\log(5^2)+ \log(2)\cdot \log(2) \\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot \log(2) + \log(2)\cdot\log(5^2)\\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot \log(2) + 2\cdot \log(2)\cdot\log(5)\\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot [~ \log(2) + \log(5) ~]\\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot \log(2\cdot 5) \\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot \log(10) \qquad | \qquad \log_{10}(10) = 1\\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \cdot 1\\ &=& 2\cdot\log(5)+ 2\cdot \log(2) \\ &=& 2\cdot [~ \log(5)+ \log(2) ~] \\ &=& 2\cdot \log(5\cdot 2) \\ &=& 2\cdot \log(10) \qquad | \qquad \log_{10}(10) = 1\\ &=& 2\cdot 1\\ &=& 2 \\ && \mathbf{ \log(25)+ \log(2) \cdot \log(50)+[\log(2)]^2 = 2 } \end{array} } \)

Spitze heureka! Greeting asinus :- )

log25+log2xlog50+(log2)^2=?

Vielen Dank asinus.

(Thank you asinus)

log25+log2xlog50+(log2)^2=?

log 25   + [ log 2 ] [log 50] + [log 2 ] [log 2]   =

log [100/4]  + [log2] [ log 100/2] + [log2] [log2]   =

log100  - log 4  + [log2] [ log 100 - log 2] + [log2] [log 2]   =

log100  - log 4  + [log100] [ log 2] - [ log 2] [ log 2] + [log2] [log 2]

2  - log 2^2  + 2log2 -   [ log 2] [log2]  + [log2] [ log 2]  =

2 - log2^2 + log2^2  =

2