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)

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

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 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)