Solve for b (3/7)^b=9

Math
(37)b=9
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln((37)b)=ln(9)
Expand the left side.
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Expand ln((37)b) by moving b outside the logarithm.
bln(37)=ln(9)
Rewrite ln(37) as ln(3)-ln(7).
b(ln(3)-ln(7))=ln(9)
b(ln(3)-ln(7))=ln(9)
Use the quotient property of logarithms, logb(x)-logb(y)=logb(xy).
bln(37)=ln(9)
Divide each term by ln(37) and simplify.
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Divide each term in bln(37)=ln(9) by ln(37).
bln(37)ln(37)=ln(9)ln(37)
Cancel the common factor of ln(37).
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Cancel the common factor.
bln(37)ln(37)=ln(9)ln(37)
Divide b by 1.
b=ln(9)ln(37)
b=ln(9)ln(37)
b=ln(9)ln(37)
The result can be shown in multiple forms.
Exact Form:
b=ln(9)ln(37)
Decimal Form:
b=-2.59321388…
Solve for b (3/7)^b=9

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