Solve for n 4550=2700(1+(0.09/400))^(4n)

Math
4550=2700(1+(0.09400))4n
Rewrite the equation as 2700(1+0.09400)4n=4550.
2700(1+0.09400)4n=4550
Simplify.
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Divide 0.09 by 400.
2700(1+0.000225)4n=4550
Add 1 and 0.000225.
2700⋅1.0002254n=4550
2700⋅1.0002254n=4550
Divide each term by 2700 and simplify.
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Divide each term in 2700⋅1.0002254n=4550 by 2700.
2700⋅1.0002254n2700=45502700
Cancel the common factor of 2700.
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Cancel the common factor.
2700⋅1.0002254n2700=45502700
Divide 1.0002254n by 1.
1.0002254n=45502700
1.0002254n=45502700
Cancel the common factor of 4550 and 2700.
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Factor 50 out of 4550.
1.0002254n=50(91)2700
Cancel the common factors.
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Factor 50 out of 2700.
1.0002254n=50⋅9150⋅54
Cancel the common factor.
1.0002254n=50⋅9150⋅54
Rewrite the expression.
1.0002254n=9154
1.0002254n=9154
1.0002254n=9154
1.0002254n=9154
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(1.0002254n)=ln(9154)
Expand ln(1.0002254n) by moving 4n outside the logarithm.
4nln(1.000225)=ln(9154)
Divide each term by 4ln(1.000225) and simplify.
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Divide each term in 4nln(1.000225)=ln(9154) by 4ln(1.000225).
4nln(1.000225)4ln(1.000225)=ln(9154)4ln(1.000225)
Simplify 4nln(1.000225)4ln(1.000225).
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Cancel the common factor of 4.
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Cancel the common factor.
4nln(1.000225)4ln(1.000225)=ln(9154)4ln(1.000225)
Rewrite the expression.
nln(1.000225)ln(1.000225)=ln(9154)4ln(1.000225)
nln(1.000225)ln(1.000225)=ln(9154)4ln(1.000225)
Cancel the common factor of ln(1.000225).
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Cancel the common factor.
nln(1.000225)ln(1.000225)=ln(9154)4ln(1.000225)
Divide n by 1.
n=ln(9154)4ln(1.000225)
n=ln(9154)4ln(1.000225)
n=ln(9154)4ln(1.000225)
n=ln(9154)4ln(1.000225)
The result can be shown in multiple forms.
Exact Form:
n=ln(9154)4ln(1.000225)
Decimal Form:
n=579.92685415…
Solve for n 4550=2700(1+(0.09/400))^(4n)

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