Given log 3 = 0.477 and log 7 = 0.845, determine the approximate value of log (132 300) without using a calculator.
All I could think about is using the antilog of each, but then how can I estimate from there?
Thank you! :)
+288 https://web2.0calc.com/questions/determining-the-approx-value-of-this-logarithm
This will help but not give you the answer. I myself don't know how to do this.
+128407 Note that 1323 factors as 3^3 * 7^2
So 1323 * 100 = 132,300 = 3^3 * 7^2 * 100 = 3^3 * 7^2 * 10^2
So....we have
log (132300) =
log ( 3^3 * 7^2 * 10^2) using a log property that log (a * b * c) = log a + log b + log c
log 3^3 + log 7^2 + log 10^2 and another property says that log a^b = b log a
3log3 + 2 log 7 + 2* log 10 = [ log 10 = 1 ]
3 (.477) + 2 (.845) + 2(1) ≈
5.121
