Solve for n (12000)=9500(1+0.06)^n

Math
(12000)=9500(1+0.06)n
Rewrite the equation as 9500(1+0.06)n=12000.
9500(1+0.06)n=12000
Add 1 and 0.06.
9500⋅1.06n=12000
Divide each term by 9500 and simplify.
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Divide each term in 9500⋅1.06n=12000 by 9500.
9500⋅1.06n9500=120009500
Cancel the common factor of 9500.
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Cancel the common factor.
9500⋅1.06n9500=120009500
Divide 1.06n by 1.
1.06n=120009500
1.06n=120009500
Cancel the common factor of 12000 and 9500.
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Factor 500 out of 12000.
1.06n=500(24)9500
Cancel the common factors.
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Factor 500 out of 9500.
1.06n=500⋅24500⋅19
Cancel the common factor.
1.06n=500⋅24500⋅19
Rewrite the expression.
1.06n=2419
1.06n=2419
1.06n=2419
1.06n=2419
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(1.06n)=ln(2419)
Expand ln(1.06n) by moving n outside the logarithm.
nln(1.06)=ln(2419)
Divide each term by ln(1.06) and simplify.
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Divide each term in nln(1.06)=ln(2419) by ln(1.06).
nln(1.06)ln(1.06)=ln(2419)ln(1.06)
Cancel the common factor of ln(1.06).
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Cancel the common factor.
nln(1.06)ln(1.06)=ln(2419)ln(1.06)
Divide n by 1.
n=ln(2419)ln(1.06)
n=ln(2419)ln(1.06)
n=ln(2419)ln(1.06)
The result can be shown in multiple forms.
Exact Form:
n=ln(2419)ln(1.06)
Decimal Form:
n=4.00925396…
Solve for n (12000)=9500(1+0.06)^n

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