If log 2=0.3010and log=0.6990.find log40
It is a good thing that I know enough about logs to correct your typo
and say log 5 = .6990
log 40 = log (8*5)
= log8 + log5
= log 2^3 + log 5
= 3log2 + log5
= 3(.3010) + .6990
= .9030 + .6990
= 1.6020
log40 = log4 + log10 = 2*0.310 + 1 = 1.6020
Well, log40 can be calculated using log properties. We can rewrite it as log(2^3 * 5), which further simplifies to log(8) + log(5).
Now, since log 2 = 0.3010, log 8 would be three times that, which is 0.9030. And since log 5 = 0.6990, we can add them up to get log40.
But hey, don't worry about the math! Just remember, when life gives you logarithms, make log-a-rithm sandwiches!
To find log 40, we can use the properties of logarithms.
First, we need to find the logarithm of the prime factors of 40, which are 2 and 5.
Using the property of logarithms that states log(ab) = log(a) + log(b), we can find the logarithm of 40.
log 40 = log(2 x 20)
Since log 2 = 0.3010, we can substitute it in:
log 40 = log 2 + log 20
Next, we can find the logarithm of 20 in a similar manner as above:
log 20 = log(2 x 10)
Substituting the value of log 2:
log 20 = log 2 + log 10
Since log 10 = 1, we have:
log 20 = log 2 + 1
Now, substituting the value of log 2 = 0.3010:
log 20 = 0.3010 + 1
log 20 = 1.3010
Finally, substituting the value of log 20 in the original equation:
log 40 = log 2 + log 20
log 40 = 0.3010 + 1.3010
log 40 = 1.6020
Therefore, log 40 is approximately equal to 1.6020.
To find log 40, we can use the property of logarithms that says log(a * b) = log(a) + log(b). In this case, we can break down 40 into its prime factors: 40 = 2 * 2 * 2 * 5.
Now, let's find the logarithm of each factor separately:
log(2) = 0.3010 (given)
log(5) = ?
We don't have the logarithm of 5, but we can approximate it based on the given logarithms. We know that log(2) > log(1) = 0 and log(2) < log(10) = 1. Therefore, we can estimate that 0 < log(5) < 1.
Next, we can use the property of logarithms mentioned earlier: log(40) = log(2 * 2 * 2 * 5) = log(2) + log(2) + log(2) + log(5).
Substituting the given values, we get:
log(40) = 0.3010 + 0.3010 + 0.3010 + log(5)
Since log(5) is unknown, we expressed it as log(5). Therefore, we can say:
log(40) ≈ 0.3010 + 0.3010 + 0.3010 + log(5)
Simplifying:
log(40) ≈ 0.9048 + log(5)
So, the value of log(40) is approximately 0.9048 + log(5).