Given that log 2 =0.3010 , log 3 =0.4771 and log5 = 0.6990 , find log 6.5 + log 4
But you do not know what log 1.0833 is!
I think this problem has a typo; it has appeared at other times, asking for
log6.25 + log4
In that case, since 6.25 = 25/4,
log6.25 + log4 = log25 - log4 + log4 = log25
= log(5^2) = 2log5 = 1.398
You are correct, my apologies for the confusion. In the case of log 6.25 + log 4, using the property of logarithms log(a*b) = log(a) + log(b), we can simplify it as log (6.25 * 4) which is equal to log 25.
Since 25 = 5^2, we can rewrite it as 2log5 = 2*0.6990 = 1.398. Thank you for pointing out the error.
We know that log 6.5 + log 4 = log(6.5 * 4).
Since 6.5 = 2 * 3.25, we can rewrite this as log(2 * 3.25 * 4).
Using the properties of logarithms, we can further simplify this expression: log(2 * 3.25 * 4) = log(2) + log(3.25) + log(4).
Now, we can substitute the given logarithmic values into the expression:
log(2) + log(3.25) + log(4) = 0.3010 + log(3.25) + 0.4771.
To find log(3.25), we can rewrite it as log(3.25) = log(3 * 1.0833) = log(3) + log(1.0833).
Substituting the given logarithmic values, log(3.25) = log(3) + log(1.0833) = 0.4771 + log(1.0833).
Finally, we can substitute this value back into the original expression:
0.3010 + log(3.25) + 0.4771 = 0.3010 + (0.4771 + log(1.0833)) + 0.4771.
Simplifying further, we get:
0.3010 + 0.4771 + log(1.0833) + 0.4771 = 0.3010 + 0.4771 + 0.4771 + log(1.0833).
Calculating the sum, we get:
0.3010 + 0.4771 + 0.4771 + log(1.0833) = 1.7323 + log(1.0833).