Solve for n 27*5^3=15^n

Math
27⋅53=15n
Rewrite the equation as 15n=27⋅53.
15n=27⋅53
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(15n)=ln(27⋅53)
Expand ln(15n) by moving n outside the logarithm.
nln(15)=ln(27⋅53)
Simplify ln(27⋅53).
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Raise 5 to the power of 3.
nln(15)=ln(27⋅125)
Multiply 27 by 125.
nln(15)=ln(3375)
nln(15)=ln(3375)
Divide each term by ln(15) and simplify.
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Divide each term in nln(15)=ln(3375) by ln(15).
nln(15)ln(15)=ln(3375)ln(15)
Cancel the common factor of ln(15).
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Cancel the common factor.
nln(15)ln(15)=ln(3375)ln(15)
Divide n by 1.
n=ln(3375)ln(15)
n=ln(3375)ln(15)
n=ln(3375)ln(15)
The result can be shown in multiple forms.
Exact Form:
n=ln(3375)ln(15)
Decimal Form:
n=3
Solve for n 27*5^3=15^n

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