# Solve for m natural log of (150mmhg)/(220mmhg)=-k*150 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.
Exponentiation and log are inverse functions.
150m⋅mhg220m⋅mhg=e-k⋅150
Multiply m by m by adding the exponents.
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.
Move m.
150m2hg220(m⋅m)hg
Multiply m by m.
150m2hg220m2hg
150m2hg220m2hg=e-k⋅150
Cancel the common factor of 150 and 220.
Factor 10 out of 150m2hg.
10(15m2hg)220m2hg
Cancel the common factors.
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.
Cancel the common factor.
15m2hg22m2hg
Rewrite the expression.
15hg22hg
15hg22hg=e-k⋅150
Cancel the common factor of h.
Cancel the common factor.
15hg22hg
Rewrite the expression.
15g22g
15g22g=e-k⋅150
Cancel the common factor of g.
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
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.
Divide each term in -150k=ln(1522) by -150.
-150k-150=ln(1522)-150
Cancel the common factor of -150.
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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