Rearranging logarithmic equation I've tried hard to rearrange the following equation to calculate t

Kassandra Ross

Kassandra Ross

Answered question

2022-06-20

Rearranging logarithmic equation
I've tried hard to rearrange the following equation to calculate the (AGE)
μ = 18.8144 + ( 1.8443 log ( age ) ) + ( 1.4032 log ( SBP ) ) + ( 0.3899 Smoke ) + ( 0.5390 log ( TC / HDL ) ) .
For example if someone with μ = 3.13422, SBP = 140, smoke = 1, and TC / HDL = 5
The age will be 55 years, But I could not arrange it in an appropriate way to get the right results.
Could you please help?

Answer & Explanation

zalitiaf

zalitiaf

Beginner2022-06-21Added 27 answers

Hopefully the process will become clear if we generalize the expression with some arbitrary constants:
μ = 18.8144 + ( 1.8443 log ( age ) ) + ( 1.4032 log ( SBP ) ) + ( 0.3899 Smoke ) + ( 0.5390 log ( TC / HDL ) )
is isomorphically converted to:
a = b c log d + E log f + g h + i log j
and we want to solve for d = age. Note how the mathematical constant e is NOT used as the coefficients/arguments in the above expression; we will need e 2.71828... later to solve for d.
Solving for ("isolating") d:
a = b c log d + E log f + g h + i log j a b E log f g h i log j = c log d c log d = a b E log f g h i log j c log d = a + b + E log f + g h + i log j log d = a + b + E log f + g h + i log j c d = e ( a + b + E log f + g h + i log j c )
I suggest labeling each constant a = μ , b = 18.8144 , c = 1.8443 , e t c . ) and then plugging in the values when you have d = age on side of the equation.
rigliztetbf

rigliztetbf

Beginner2022-06-22Added 7 answers

The natural logarithm log : R + R is the inverse of the exponential function exp : R R + . This means that for any positive x, exp ( log x ) ( = e log x ) = x

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