Question

2. The log3 20 can be written as

(1) 2log, 2+ log, 5
(3) log, 15+log, 5
(2) 2 log, 10
(4) 2log, 4+3log, 4

Answer 1

The expression log3 20 can be written as 2log3 2 + log3 5.

Step-by-step explanation:

The expression log3 20 can be written as 2log10 + log5. This answer is represented by option (1).

To understand why, we can use the properties of logarithms. The property states that log(aᵇ) = b * log(a), where a is the base and b is the exponent. In this case, we have log3 20.

1. We can rewrite 20 as 2² * 5. This is because 20 can be factored into 4 * 5.
2. Using the property mentioned earlier, we can rewrite log3 20 as log3 (2² * 5) = 2 * log3 2 + log3 5.

Therefore, the correct representation is 2log3 2 + log3 5, which matches option (1).

Answer 2

`2\log _32+\log _35`

Step-by-step explanation:

Given:
`\log _3 20`

To find: the correct option

Solution:

The logarithm function is the inverse function to exponentiation function.

Domain of a logarithmic function = set of real numbers greater than zero Range of a logarithmic function = set of real numbers

`\log _3 20=\log _3(2^2* 5)`

As
`\log _a(xy)=\log _ax+\log _ay`,

`\log _3 20=\log _32^2+\log _35`

As
`\log _ax^y=y\log _ax` ,

`\log _3 20=\log _32^2+\log _35\\=2\log _32+\log _35`