SOLUTION: Please help me solve this equation: {{{ 2.79^(x-1) - 4.377^x = 0 }}}. Thank you!
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Question 169886: Please help me solve this equation: . Thank you!
Found 2 solutions by Alan3354, gonzo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
(x-1)*log(2.79) = x*log(4.377)
(x-1)*0.4456 = x*0.6412
0.4456x - 0.4456 = 0.6412x
-0.4456 = 0.19557x
x = -2.2785
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
problem:
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not sure if this is the correct way to approach this, but i got a solution and it appears to be good.
-----
you start off with:
add 4.377^x to both sides of the equation:
raise both sides of the equation to the exponent.
your equation becomes:
simplify this and it becomes:
which is the same as:
-----
now that you have this in a standard exponential form, you should be able to solve it using logarithms.
you make use of two logarithmic formulas:
first formula:
if and only if
second formula:
-----
using the first formula, your formula of:
becomes:
----
using the second formula,
becomes:
-----
this becomes:
let the letter "a" represent ".69497895" for now to make simplifying easier to show.
equation becomes:
multiply both sides of equation by (x-1)
simplify:
add a to both sides of equation and subtract x from both sides of equation:
factor out the x:
divide both sides by (a-1)
replace a with .69497895 and solve"
-----
plug that value of x into your original equation:
becomes:
you will find the answer to be 0 proving the value of x is correct.
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i may have messed up the digits but the real values were stored in the calculator and are accurate.
the values should be:
.69497895 for a
-.30502105 for 1-a
-2.278462259 for x
any deviation from these numbers above is a typo.
-----
there might be an easier way to do this but i don't see it right now.
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