find log30 if log2=0.301 and log3=o.477
log 30
= log( 3 x 10)
= log 3 + log 10
= .477 + 1
= 1.477
looks like the log2 was not needed, but the question probably contained other cases where it might be needed
e.g.
log 60
= log (3 x 2 x 10)
= log 3 + log 2 + log 10
etc
To find the value of logarithm log30, given the values of log2 and log3, we can use the logarithmic properties and a mathematical formula.
First, we know that log30 can be written as log(2 × 3 × 5). This is because prime factorizing 30 gives us 2 × 3 × 5.
Next, let's use the logarithmic property log(ab) = log(a) + log(b).
So, log30 can be written as log(2) + log(3) + log(5).
Given the values log2 = 0.301 and log3 = 0.477, we can substitute them into the equation:
log30 = log(2) + log(3) + log(5)
= 0.301 + 0.477 + log(5)
Since we don't have the value of log5, we cannot directly substitute it. However, we can calculate log5 using the same logarithmic property.
We know that log5 can be written as log(10 ÷ 2), because 10 is equal to 2 × 5.
Using the logarithmic property log(ab) = log(a) + log(b):
log5 = log(10 ÷ 2)
= log(10) - log(2)
Given that log10 = 1 and log2 = 0.301, we can substitute them into the equation:
log5 = log(10) - log(2)
= 1 - 0.301
= 0.699
Now that we have the value of log5, we can substitute it back into the equation for log30:
log30 = 0.301 + 0.477 + log(5)
= 0.301 + 0.477 + 0.699
= 1.477
Therefore, log30 is approximately 1.477.