Use log 3=0.477 and log 5=0.699 to evaluate the logarithm.
log45
45 = 3 * 3 * 5
log(45) = 2 log(3) + log(5)
45 = 3 * 3 *5
so
log 45 = log (3*3*5)
and we all know
log (a*b*c) = log a + log b + log c
To evaluate the logarithm of 45 using the given logarithmic values, we can use the logarithmic property of addition. The property states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.
Here's how we can compute log 45 using the given values:
1. Start by breaking down 45 into its prime factors: 45 = 3 * 3 * 5.
2. Apply the logarithmic property of addition to find the logarithm of each factor.
- log 3 = 0.477
- log 5 = 0.699
3. Since 45 can be expressed as 3 * 3 * 5, we can write it as log 45 = log (3 * 3 * 5).
4. Using the logarithmic property, we can rewrite this as log 45 = log 3 + log 3 + log 5.
5. Substitute the values obtained from step 2 into the equation:
- log 45 = 0.477 + 0.477 + 0.699.
6. Simplify the expression by adding the values together:
- log 45 ≈ 1.431.
Thus, the value of log 45, based on the given logarithmic values, is approximately 1.431.
To evaluate log45 using the given logarithmic values, we can use the logarithm rules to simplify the expression.
The logarithm rule states that log(ab) = log(a) + log(b).
Using this rule, we can rewrite log45 as log(9 * 5).
Next, we can use the logarithm rule again to split this expression into two separate logarithms:
log(9 * 5) = log(9) + log(5).
We now have two logarithms: log(9) and log(5), for which we have the values log 3 = 0.477 and log 5 = 0.699, respectively.
Substituting these values into the equation, we get:
log(9) + log(5) = 0.477 + 0.699
Adding the two values together gives us the final result:
log45 = 1.176.