You can do even better if you memorize three numbers: 301, 477, 845. These are the values of 1000log10(n) for n = 2, 3, 7. From these you can quickly get the values for 4 (= 22), 5 (=10/2), 6 (=23), 8 (=222) and 9 (=33).
For your example 1.49 is close to 3 / 2 so the log will be very close 0.477 - 0.301 = 0.176.
This means that your answer is near 8.176 (actual value is 8.173).
This tiny table of logs can also let you answer parlor trick questions like what is the first digit of 2^1000 (the result is very nearly 10^301 but a bit above, so 1 is the leading digit).
For your example 1.49 is close to 3 / 2 so the log will be very close 0.477 - 0.301 = 0.176.
This means that your answer is near 8.176 (actual value is 8.173).
This tiny table of logs can also let you answer parlor trick questions like what is the first digit of 2^1000 (the result is very nearly 10^301 but a bit above, so 1 is the leading digit).