How do you solve this problem?
1 answer:
Answer: 2.5722 .
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Explanation:
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log(base "
" of 19 = y ? ; Solve for "y" ;
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^ (y) = 19 ; Solve for "y" ?
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Take the "ln" (that is, "natural logarithm", of both sides:
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ln [ ^ (y) ] = ln 19 ;
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y * ln = ln 19 .
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Use "3.1416" as an approximation for: " " ;
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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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_____________________________________________________
Explanation:
_________________________________________________
log(base "
__________________________________________________
__________________________________________________
Take the "ln" (that is, "natural logarithm", of both sides:
__________________________________________________
ln [
__________________________________________________
y * ln
__________________________________________________
Use "3.1416" as an approximation for: "
__________________________________________________
y * ln (3.1416) = ln 19 ;
__________________________________________________
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) ;
_________________________________________________________
y * ln (3.1416) / [ ln (3.1416) ] = ln 19 / [ ln (3.1416) ] ;
________________________________________________________
y = ln 19 / [ ln (3.1416) ] ;
_______________________________________________________
y = 2.5721639670047041 ;
→ round to nearest 4 (FOUR) decimal places;
_______________________________________________________
→ y = 2.5722 .
________________________________________________________
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<h3>Answer: Choice B) x = 65, y = 10</h3>
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Work Shown:
The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so
(2x-y)+60 = 180
2x-y = 180-60 ... subtract 60 from both sides
2x-y = 120 ... call this equation 1
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Similarly, (2x+y) and 40 also combine to 180
(2x+y) + 40 = 180
2x+y = 180-40 ... subtract 40 from both sides
2x+y = 140 ... call this equation 2
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Line up equation 1 and equation 2. Then add straight down
That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.
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If x = 65, then,
2x-y = 120
2(65)-y = 120
130 - y = 120
-y = 120-130
-y = -10
y = 10
or
2x+y = 140
2(65)+y = 140
130+y = 140
y = 140-130
y = 10
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Either way end up with x = 65 and y = 10