If log 2=0.3010,log 3= 0.4771 and log 5=0.6990 find log(0.125)
We can use the properties of logarithms to solve this problem. First, recall that the logarithm of a number is the power to which the base must be raised to equal that number.
Given that log 2 = 0.3010, we can rewrite the logarithm of any power of 2 as a product of the logarithm of 2. Using this property, we can calculate:
log 4 = log (2^2) = 2 * log 2 = 2 * 0.3010 = 0.6020
Similarly, given that log 3 = 0.4771, we can rewrite the logarithm of any power of 3 as a product of the logarithm of 3. Using this property, we can calculate:
log 9 = log (3^2) = 2 * log 3 = 2 * 0.4771 = 0.9542
Now, log (0.125) can be expressed as a power of 2 by using the fact that 0.125 = 2^(-3). Thus:
log (0.125) = log (2^(-3)) = -3 * log 2 = -3 * 0.3010 = -0.9030
Therefore, log (0.125) is approximately -0.9030.