Question

How do you solve this problem?

Answer 1

Answer:  2.5722 .
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 Explanation:
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              log(base "$\pi$" of 19  = y ?  ;  Solve for "y" ;
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     $\pi$ ^ (y)  = 19 ;  Solve for "y" ?
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Take the "ln" (that is, "natural logarithm", of both sides:
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           ln  [ $\pi$ ^ (y) ]  = ln 19  ;
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             y *  ln $\pi$ = ln 19 .
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     Use "3.1416" as an approximation for:  " $\pi$ "  ;
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             y * ln (3.1416) = ln 19 ;
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  Divide EACH side of the equation by:  " [ ln (3.1416) ]" ; to isolate "y" on one side of the equation; and to solve for "y";  (Use a calculator to do this) ;
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            y *  ln (3.1416)  / [ ln (3.1416) ] = ln 19 / [ ln (3.1416) ] ;
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           y = ln 19 / [ ln (3.1416) ] ;
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           y = 2.5721639670047041 ; 
 
                  → round to nearest 4 (FOUR) decimal places;
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         → y = 2.5722 .
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