a bakery supplier receives an order for 2 tonsof sugar from a bakery change. The sugar is shipped in the crates. Each crate hold
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Factor completely x³ + 6x² - 3x – 18
with a root of x = -6
the answer is 210
with a root of x = -6
the answer is 210
Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
Answer:
Step-by-step explanation:
We want to find the sum of
We can rewrite this as
This becomes;
Recall that;
This implies that;
Combine like terms: