Using log2=.3010 and log5=.6990 compute
log2000000.
100000/5 = 20000 so I just did 20000*.699 = 13980 and then added .301 which equals 13980.3
^I know that was wrong
log2000000 = log 2 + log 10^6 = 6.301
or,
2,000,000 = 10,000,000/5, so
log 10^7 - log5 = 7-.699 = 6.301
thanks that makes sense
To compute log2000000 using the given logarithmic values, we can use the log rules. The rule we can apply here is log(xy) = log(x) + log(y).
First, let's break down 2000000 into its prime factors:
2000000 = 2^6 * 5^6
Using the log rule, we can rewrite log2000000 as:
log(2^6 * 5^6) = log(2^6) + log(5^6)
Now, substitute log2 = 0.3010 and log5 = 0.6990:
log(2^6) + log(5^6) = 6 * log2 + 6 * log5
Now, plug in the values:
6 * 0.3010 + 6 * 0.6990 = 1.8060 + 4.1940 = 5.9990
Therefore, log2000000 is approximately 5.9990.