if log3=a then log300 can be expressed as?
1) 100a
2)a+2
3)100+a
4)3a
log 300 = log 3 + log 100 = a+2
To express log300 in terms of log3, we can use the logarithmic property that states log(a^n) = n*log(a).
Given log3 = a, we can rewrite log300 as log(3^2 * 10^2).
Using the property mentioned above, we can rewrite this as:
log(3^2) + log(10^2).
Applying the property again, we get:
2log3 + 2log10.
Now, the logarithm of 10 is a commonly known value, which is 1. Therefore, we can simplify the expression further:
2log3 + 2(1).
Simplifying the expression:
2log3 + 2.
Therefore, log300 can be expressed as 2log3 + 2.
None of the given options (1) 100a, 2) a+2, 3) 100+a, 4) 3a) match this expression.
To solve this question, we need to use the laws of logarithms. Let's start by using the property that states the logarithm of a product is equal to the sum of the logarithms of the individual factors:
log(a * b) = log(a) + log(b)
In this case, we have log300. We can rewrite 300 as the product of two numbers: 3 and 100.
log(3 * 100) = log(3) + log(100)
Now, let's substitute log3 with its given value, which is a:
log(3) + log(100) = a + log(100)
Since log(100) can be rewritten as log(10^2) = 2 log(10), and log(10) = 1, we can simplify the expression further:
a + log(100) = a + 2
Therefore, log300 can be expressed as (a + 2), so the correct answer is option 2) a+2.