Question

2. Statement(A): The non terminating decimal form of a real number is an irrational number.
Statement(B): The standard base of a logarithm is 10.
A) Both A and B are true
B) Both A and B are false
C) A is true and B is false
D) A is false and B is true​

Answer 1

Answer...(D) A is false and B is true

Answer 2

Answer:

The Correct answer is option A

Step-by-step explanation:

Statement  (A)

The number which has an infinite number of digits after the decimal point without any pattern of repetition of digits is known as non-terminating non-recurring decimal.

Non-terminating non-recurring decimals are also known as irrational numbers.

Here are some examples

(i) 0.212212221 . . .

(ii) 0.03003000300003 . . .

(iii) 0.825882588825 . . .

Statement (B)

Natural logs are different than common logarithms .The base of a natural logarithm is the special number “e” and it is a irrational number that is equivalent to 2.718182845.logarithms to base 10 are called common logarithms. Another important base e to logarithms are called natural log.

Examples

1.common logarithms

Log y=x

y=10^x

2.natural logarithms

In y=X

y=e^x

3.log base 2

In binary logarithms the base 2 is the power to which the number 2 must be raised to obtain the value n .The binary logarithm function is the inverse function of the power of two function.

Properties:

Log 2(xy)= log2(x)+log2(y)

Log2(x/y)=log2(x)-log2(y)

Log2(x^y)=ylog2(x).

The conversion of log with base e i.e natural log to log with base 10 is as follows

Log base e= log base 10/ log of e with base 10

Thus conversion is

Log base e *(log e with base 10)=log base 10

Thus the property used here is

Log x base y= log x base m / log y base m.

Reference Link

• https://brainly.in/question/15896939