Solve for m natural log of (150mmhg)/(220mmhg)=-k*150

Math
ln(150mmhg220mmhg)=-k⋅150
To solve for m, rewrite the equation using properties of logarithms.
eln(150m⋅mhg220m⋅mhg)=e-k⋅150
Simplify the left side.
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Exponentiation and log are inverse functions.
150m⋅mhg220m⋅mhg=e-k⋅150
Multiply m by m by adding the exponents.
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Move m.
150(m⋅m)hg220m⋅mhg
Multiply m by m.
150m2hg220m⋅mhg
150m2hg220m⋅mhg=e-k⋅150
Multiply m by m by adding the exponents.
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Move m.
150m2hg220(m⋅m)hg
Multiply m by m.
150m2hg220m2hg
150m2hg220m2hg=e-k⋅150
Cancel the common factor of 150 and 220.
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Factor 10 out of 150m2hg.
10(15m2hg)220m2hg
Cancel the common factors.
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Factor 10 out of 220m2hg.
10(15m2hg)10(22m2hg)
Cancel the common factor.
10(15m2hg)10(22m2hg)
Rewrite the expression.
15m2hg22m2hg
15m2hg22m2hg
15m2hg22m2hg=e-k⋅150
Cancel the common factor of m2.
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Cancel the common factor.
15m2hg22m2hg
Rewrite the expression.
15hg22hg
15hg22hg=e-k⋅150
Cancel the common factor of h.
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Cancel the common factor.
15hg22hg
Rewrite the expression.
15g22g
15g22g=e-k⋅150
Cancel the common factor of g.
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Cancel the common factor.
15g22g
Rewrite the expression.
1522
1522=e-k⋅150
1522=e-k⋅150
Multiply 150 by -1.
1522=e-150k
Solve for m
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Since k is on the right side of the equation, switch the sides so it is on the left side of the equation.
e-150k=1522
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(e-150k)=ln(1522)
Use logarithm rules to move -150k out of the exponent.
-150kln(e)=ln(1522)
The natural logarithm of e is 1.
-150k⋅1=ln(1522)
Multiply -150 by 1.
-150k=ln(1522)
Divide each term by -150 and simplify.
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Divide each term in -150k=ln(1522) by -150.
-150k-150=ln(1522)-150
Cancel the common factor of -150.
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Cancel the common factor.
-150k-150=ln(1522)-150
Divide k by 1.
k=ln(1522)-150
k=ln(1522)-150
Move the negative in front of the fraction.
k=-ln(1522)150
k=-ln(1522)150
k=-ln(1522)150
The result can be shown in multiple forms.
Exact Form:
k=-ln(1522)150
Decimal Form:
k=0.00255328…
Solve for m natural log of (150mmhg)/(220mmhg)=-k*150

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