Logarithm Calculations
In this article, we will explore three logarithm calculations: 1/2 log 9, 1/3 log 7, and 49 log 32.
1/2 log 9
To calculate 1/2 log 9, we need to use the property of logarithms that states:
log(a^b) = b * log(a)
In this case, we can rewrite 1/2 log 9 as:
1/2 log 9 = log(9^(1/2))
Using the fact that 9^(1/2) = 3, we get:
1/2 log 9 = log(3)
1/3 log 7
To calculate 1/3 log 7, we can use the same property of logarithms as before:
1/3 log 7 = log(7^(1/3))
Using the fact that 7^(1/3) = ∛7, we get:
1/3 log 7 = log(∛7)
49 log 32
To calculate 49 log 32, we can use the property of logarithms that states:
a * log(b) = log(b^a)
In this case, we can rewrite 49 log 32 as:
49 log 32 = log(32^49)
Using the fact that 32 = 2^5, we get:
49 log 32 = log((2^5)^49)
= log(2^(245))
Therefore, the three logarithm calculations are:
- 1/2 log 9 = log(3)
- 1/3 log 7 = log(∛7)
- 49 log 32 = log(2^(245))
