Which of the following statements is NOT true regarding an expression written in scientific notation in teh form of a x 10^n?
2 answers:
Answer:
Option C
Step-by-step explanation:
Given : An expression written in scientific notation in the form of
Let
To find : Which statement is not true for the expression.
Solution : is a power, with a base of 10 and an exponent of "b".
''n" is associate whole number like the quantity of places the decimal "moves".
→ When the exponent "n" is positive (and not zero), the number "x" is greater than one.
→ The larger the exponent "n", the larger the number "x".
→ When the exponent "n" is negative, the number "x" is between zero and one.
→ The smaller the exponent "n", the nearer the quantity "x" is to zero.
From the above statements we say that Option C - Doubling n results in a doubling of the value of the expression is incorrect or not true
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Answer:
Step-by-step explanation:
So, there are two logarithmic identities you're going to need to know.
<em>Logarithm of a power</em>:
So to provide a quick proof and intuition as to why this works, let's consider the following logarithm:
Now if we raise both sides to the power of c, we get the following equation:
Using the exponential identity:
We get the equation:
If we convert this back into logarithmic form we get:
Since x was the basic logarithm we started with, we substitute it back in, to get the equation:
Now the second logarithmic property you need to know is
<em>The Logarithm of a Product</em>:
Now for a quick proof, let's just say:
Now rewriting them both in exponential form, we get the equations:
We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:
Using the exponential identity: , we can rewrite the equation as:
taking the logarithm of both sides, we get:
Since x and y are just the logarithms we started with, we can substitute them back in to get:
Now let's use these identities to rewrite the equation you gave
As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)
Now using the logarithm of a power to rewrite the log(x^2) we get:
V of w sphere = 
r³
Multiply by 3 on either sides to get rid of the fraction.
3V = 4r³
Now divide either sides by 4 to isolate r³
r³
4
and 4 cancels out
= r³
Take the cube root to isolate r.
![\sqrt[3]{ \frac{3V}{4 \pi } } = \sqrt[3]{r^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B3V%7D%7B4%20%5Cpi%20%7D%20%7D%20%3D%20%20%5Csqrt%5B3%5D%7Br%5E3%7D%20)
the cube root cancels the cube
![\sqrt[3]{ \frac{3V}{4 \pi } }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B3V%7D%7B4%20%5Cpi%20%7D%20%7D%20)
= r
Multiply by 3 on either sides to get rid of the fraction.
3V = 4
Now divide either sides by 4
4
Take the cube root to isolate r.
the cube root cancels the cube