Question

Вычислите1)Log4 Log3 81 2)Log9 Log4 64Решите уравнение1)4в квадрате -9*2х+18=02)9в квадрате -8*3в квадрате+17=0Решить задачу1)из 225кл. руды получается 34,2кг. меди Каково процентное содержание меди в руде?

Answer 1

$log_{4}log_{3}81=log_{4}log_{3}3^4=log_{4}(4log_{3}3)=log_{4}4=1$

$log_{9}log_{4}64=log_{9}log_{4}4^3=log_{9}(3log_{4}4)=log_{9}3=0,5$

уравнения:

Не совсем понятно записано, потому решу двояко:

1) а)(4^2-9)*(2x+18)=0

(16-9)*(2x+18)=0

2x+18=0

2x=-18

x=-9

 

б) (без скобок) 4^2-9*2x+18=0

16-18x+18=0

-18x+34=0

-18x=-34

x=34/18=17/9

 

2) На уравнение не похоже, отсутствует переменная ))))

 

Задача:

Так как в 225 кг. руды содержится 34,2 кг. меди, то процентное содержание меди в руде равно:

(34,2:225)*100%=15,2%

Answer 2

Log₄ Log₃ 81=Log₄ Log₃ 3⁴=Log₄(4 Log₃3)=Log₄4=1

Log₉ Log₄64=Log₉Log₄4³=Log₉(3Log₄4)=Log₉3=¹/₂=0.5

4²-9*2х+18=0

16-18х+18=0

18х=34

х=1⁸/₉

если с х

4х²-9*2х+18=0

4х²-18х+18=0

D=324-288=36

х₁=(18+6)/8=3

х₂=(18-6)/8=1¹/₂

 

9х²-8*3х²+17=0

9х²-24х²+17=0

-15х²+17=0

-15х²=-17

х=√1²/₁₅

 

Составим пропорцию

225кг-100%

34,2кг-х%

х=(34,2*100)/225=15,2%

 

Answer 3

Logarithmic Calculations:

1) To calculate Log4 + Log3 + 81, we can use the properties of logarithms. The sum of logarithms with the same base is equal to the logarithm of the product of the numbers inside the logarithms. Therefore:

Log4 + Log3 + 81 = Log(4 * 3) + 81

Simplifying further:

Log4 + Log3 + 81 = Log12 + 81

Now, we need to evaluate Log12. Using the change of base formula, we can convert Log12 to a different base, such as the common logarithm (base 10) or the natural logarithm (base e). Let's use the common logarithm:

Log12 = Log(12) / Log(10)

Using a calculator, we find that Log12 is approximately 1.0791812460476247.

Substituting this value back into the original equation:

Log4 + Log3 + 81 ≈ 1.0791812460476247 + 81

Simplifying further:

Log4 + Log3 + 81 ≈ 82.07918124604762

Therefore, Log4 + Log3 + 81 ≈ 82.07918124604762.

2) Similarly, to calculate Log9 + Log4 + 64, we can use the properties of logarithms. Applying the same steps as above:

Log9 + Log4 + 64 = Log(9 * 4) + 64

Simplifying further:

Log9 + Log4 + 64 = Log36 + 64

Using the change of base formula, let's convert Log36 to the common logarithm:

Log36 = Log(36) / Log(10)

Using a calculator, we find that Log36 is approximately 1.5563025007672882.

Substituting this value back into the original equation:

Log9 + Log4 + 64 ≈ 1.5563025007672882 + 64

Simplifying further:

Log9 + Log4 + 64 ≈ 65.55630250076729

Therefore, Log9 + Log4 + 64 ≈ 65.55630250076729.

Solving Equations:

1) To solve the equation 4v^2 - 9 * 2x + 18 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the equation to the standard quadratic form, we have a = 4, b = -9 * 2, and c = 18. Substituting these values into the quadratic formula:

x = (-(-9 * 2) ± √((-9 * 2)^2 - 4 * 4 * 18)) / (2 * 4)

Simplifying further:

x = (18 ± √(324 - 288)) / 8

x = (18 ± √36) / 8

x = (18 ± 6) / 8

Therefore, the solutions to the equation are:

x1 = (18 + 6) / 8 = 24 / 8 = 3

x2 = (18 - 6) / 8 = 12 / 8 = 1.5

Hence, the solutions to the equation 4v^2 - 9 * 2x + 18 = 0 are x = 3 and x = 1.5.

2) To solve the equation 9v^2 - 8 * 3v^2 + 17 = 0, we can simplify it first:

9v^2 - 24v^2 + 17 = 0

-15v^2 + 17 = 0

Rearranging the equation:

-15v^2 = -17

Dividing both sides by -15:

v^2 = -17 / -15

v^2 = 17 / 15

Taking the square root of both sides:

v = ± √(17 / 15)

Therefore, the solutions to the equation 9v^2 - 8 * 3v^2 + 17 = 0 are v = ± √(17 / 15).

Problem Solving:

1) The problem states that from 225 kg of ore, 34.2 kg of copper is obtained. We need to find the percentage of copper in the ore.

To find the percentage, we divide the mass of copper obtained by the mass of the ore and multiply by 100:

Percentage of copper = (Mass of copper / Mass of ore) * 100

Substituting the given values:

Percentage of copper = (34.2 kg / 225 kg) * 100

Using a calculator, we find that the percentage of copper is approximately 15.2%.

Therefore, the percentage of copper in the ore is approximately 15.2%.

Please let me know if there's anything else I can help you with!