Math

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I cant figure this question out. I could use some help.

Solve for x

lnx-lnx^2+ln5 = 0

Simplify the answer

  • Math -

    Use the law of logarithms:
    ln(a)+ln(b)=ln(ab)
    ln(a)-ln(b)=ln(a/b)
    kln(a)= ln(ak)
    ln(1)=0
    ln(1/x)=-ln(x)

    so
    ln(x)-ln(x²)+ln(5)=0
    ln(x/x²)+ln(5)=0
    ln(1/x)+ln(5)=0
    -ln(x)+ln(5)=0
    ln(x)=ln(5)
    e^(ln(x))=e^(ln(5))
    x=5

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