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Vlad [161]
3 years ago
15

3.3^(2x+1)-103^x+1=0 need value of x

Mathematics
1 answer:
photoshop1234 [79]3 years ago
4 0

Answer:

The value of x is approximately -1.531.

Step-by-step explanation:

Let 3.3^{2\cdot x + 1}-103^{x+1} = 0, we proceed to solve this expression by algebraic means:

1) 3.3^{2\cdot x + 1}-103^{x+1} = 0  Given

2) 3.3^{2\cdot x}\cdot 3.3 -103^{x}\cdot 103 = 0 a^{b}\cdot a^{c} = a^{b+c}

3) (3.3^{x})^{2}\cdot 3.3 -\left[\left( \sqrt{103} \right)^{2}\right]^{x}\cdot 103 = 0 (a^{b})^{c} = a^{b\cdot c}

4) (3.3^{x})^{2}\cdot 3.3 - \left[\left(\sqrt{103}\right)^{x}\right]^{2}\cdot 103 = 0 (a^{b})^{c} = a^{b\cdot c}/Commutative property

5) \left[\left(\frac{3.3}{\sqrt{103}}\right)^{x}\right] ^{2}-\frac{103}{3.3} = 0 Existence of multiplicative inverse/Definition of division/Modulative property/a^{b}\cdot a^{c} = a^{b+c}

6) \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\frac{103}{3.3} Existence of additive inverse/Modulative property/(a^{b})^{c} = a^{b\cdot c}

7) \log \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\log \frac{103}{3.3} Definition of logarithm.

8) 2\cdot x\cdot \log \left(\frac{3.3}{\sqrt{103}} \right)= \log \frac{103}{3.3}     \log_{b} a^{c} = c\cdot \log_{b} a

9) 2\cdot x \cdot [\log 3.3-\log \sqrt{103}] = \log 103 - \log 3.3      \log_{b} \frac{a}{d}

10) x\cdot (2\cdot \log 3.3-\log 103) = \log 103 - \log 3.3     \log_{b} a^{c} = c\cdot \log_{b} a/Associative property

11) x = \frac{\log 103-\log 3.3}{2\cdot \log 3.3-\log 103}   Existence of multiplicative inverse/Definition of division/Modulative property

12) x \approx -1.531  Result

The value of x is approximately -1.531.

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The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

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Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80                              .                  .                 .    1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68               .                 .                  .        2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

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Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.

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Step-by-step explanation:

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