Answer:
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PLZ help (5x10^2)+(4x10^3)
2 answers:
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Answer:
- 3log(10) -2log(5) ≈ 1.60206
- no; rules of logs apply to any base. ln(x) ≈ 2.302585×log(x)
- no; the given "property" is nonsense
Step-by-step explanation:
<h3>1.</h3>The given expression expression can be simplified to ...
3log(10) -2log(5) = log(10^3) -log(5^2) = log(1000) -log(25)
= log(1000/25) = log(40) . . . . ≠ log(5)
≈ 1.60206
Or, it can be evaluated directly:
= 3(1) -2(0.69897) = 3 -1.39794
= 1.60206
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<h3>2.</h3>The properties of logarithms apply to logarithms of any base. Natural logs and common logs are related by the change of base formula ...
ln(x) = log(x)/log(e) ≈ 2.302585·log(x)
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<h3>3.</h3>The given "property" is nonsense. There is no simplification for the product of logs of the same base. There is no expansion for the log of a sum. The formula for the log of a power does apply:
Numerical evaluation of Mr. Kim's expression would prove him wrong.
log(3)log(4) = (0.47712)(0.60206) = 0.28726
log(7) = 0.84510
0.28726 ≠ 0.84510
log(3)log(4) ≠ log(7)
Answer:
Joint variation states that:
If z is directly proportional to x and inversely proportional to y,
i.e, ,
then the equation is in the form: where k is the constant of variation.
From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature
i.,e ,
by definition of joint variation:
.....[1] where k is the constant of variation.
It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).
Substitute these given values in [1] to solve for k;
Simplify:
Divide by 200 both sides we have;
Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.
To find the volume (V);
Now substitute the given data and value of k in [1] we have;
Therefore, the Volume of a gas is, 4 liters