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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