Solve for N N=( natural log of 200÷(200-(6000*0.18)÷12))/( natural log of 1+0.18÷12)

N=ln(200÷(200-6000⋅0.18÷12))ln(1+0.18÷12)
Reduce the expression by cancelling the common factors.
Cancel the common factor of 6000 and 12.
Factor 12 out of 6000⋅0.18.
N=ln(200200-12(500⋅0.18)12)ln(1+0.18÷12)
Cancel the common factors.
Factor 12 out of 12.
N=ln(200200-12(500⋅0.18)12(1))ln(1+0.18÷12)
Cancel the common factor.
N=ln(200200-12(500⋅0.18)12⋅1)ln(1+0.18÷12)
Rewrite the expression.
N=ln(200200-500⋅0.181)ln(1+0.18÷12)
Divide 500⋅0.18 by 1.
N=ln(200200-(500⋅0.18))ln(1+0.18÷12)
N=ln(200200-(500⋅0.18))ln(1+0.18÷12)
N=ln(200200-(500⋅0.18))ln(1+0.18÷12)
Cancel the common factor of 200 and 200-(500⋅0.18).
Reorder terms.
N=ln(200-1⋅0.18⋅500+200)ln(1+0.18÷12)
Factor 2 out of 200.
N=ln(2(100)-1⋅0.18⋅500+200)ln(1+0.18÷12)
Cancel the common factors.
Factor 2 out of -1⋅0.18⋅500.
N=ln(2(100)2(-1⋅0.09⋅500)+200)ln(1+0.18÷12)
Factor 2 out of 200.
N=ln(2⋅1002(-1⋅0.09⋅500)+2⋅100)ln(1+0.18÷12)
Factor 2 out of 2(-1⋅0.09⋅500)+2(100).
N=ln(2(100)2(-1⋅0.09⋅500+100))ln(1+0.18÷12)
Cancel the common factor.
N=ln(2⋅1002(-1⋅0.09⋅500+100))ln(1+0.18÷12)
Rewrite the expression.
N=ln(100-1⋅0.09⋅500+100)ln(1+0.18÷12)
N=ln(100-1⋅0.09⋅500+100)ln(1+0.18÷12)
N=ln(100-1⋅0.09⋅500+100)ln(1+0.18÷12)
N=ln(100-1⋅0.09⋅500+100)ln(1+0.18÷12)
Simplify the denominator.
Multiply -1 by 0.09.
N=ln(100-0.09⋅500+100)ln(1+0.18÷12)
Multiply -0.09 by 500.
N=ln(100-45+100)ln(1+0.18÷12)
N=ln(10055)ln(1+0.18÷12)
N=ln(10055)ln(1+0.18÷12)
Cancel the common factor of 100 and 55.
Factor 5 out of 100.
N=ln(5(20)55)ln(1+0.18÷12)
Cancel the common factors.
Factor 5 out of 55.
N=ln(5⋅205⋅11)ln(1+0.18÷12)
Cancel the common factor.
N=ln(5⋅205⋅11)ln(1+0.18÷12)
Rewrite the expression.
N=ln(2011)ln(1+0.18÷12)
N=ln(2011)ln(1+0.18÷12)
N=ln(2011)ln(1+0.18÷12)
Simplify the denominator.
Divide 0.18 by 12.
N=ln(2011)ln(1+0.015)
N=ln(2011)ln(1.015)
N=ln(2011)ln(1.015)
The result can be shown in multiple forms.
Exact Form:
N=ln(2011)ln(1.015)
Decimal Form:
N=40.15397680…
Solve for N N=( natural log of 200÷(200-(6000*0.18)÷12))/( natural log of 1+0.18÷12)

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