# Solve for n 100=9000^(n-1) 100=9000n-1
Rewrite the equation as 9000n-1=100.
9000n-1=100
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(9000n-1)=ln(100)
Expand ln(9000n-1) by moving n-1 outside the logarithm.
(n-1)ln(9000)=ln(100)
Simplify (n-1)ln(9000).
Apply the distributive property.
nln(9000)-1ln(9000)=ln(100)
Rewrite -1ln(9000) as -ln(9000).
nln(9000)-ln(9000)=ln(100)
nln(9000)-ln(9000)=ln(100)
Move all the terms containing a logarithm to the left side of the equation.
nln(9000)-ln(9000)-ln(100)=0
Move all terms not containing n to the right side of the equation.
Add ln(9000) to both sides of the equation.
nln(9000)-ln(100)=ln(9000)
Add ln(100) to both sides of the equation.
nln(9000)=ln(9000)+ln(100)
nln(9000)=ln(9000)+ln(100)
Divide each term by ln(9000) and simplify.
Divide each term in nln(9000)=ln(9000)+ln(100) by ln(9000).
nln(9000)ln(9000)=ln(9000)ln(9000)+ln(100)ln(9000)
Cancel the common factor of ln(9000).
Cancel the common factor.
nln(9000)ln(9000)=ln(9000)ln(9000)+ln(100)ln(9000)
Divide n by 1.
n=ln(9000)ln(9000)+ln(100)ln(9000)
n=ln(9000)ln(9000)+ln(100)ln(9000)
Cancel the common factor of ln(9000).
Cancel the common factor.
n=ln(9000)ln(9000)+ln(100)ln(9000)
Divide 1 by 1.
n=1+ln(100)ln(9000)
n=1+ln(100)ln(9000)
n=1+ln(100)ln(9000)
The result can be shown in multiple forms.
Exact Form:
n=1+ln(100)ln(9000)
Decimal Form:
n=1.50578587…
Solve for n 100=9000^(n-1)

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