+0

# Using approx. and the laws of logarithms to perform this calculation?

0
112
3

I need to simplify \((1.44)(1.2)\) using this approximation: \(log 1.44 ≈ 0.15836\).

I can only use paper and pencil to simplify this calculation.

How should I do this? Thank you! :)

Apr 29, 2019

#1
+1

Since 1.2 is the square root of 1.44, then log 1.2 =0.15836 / 2 =0.07918.

When you multiply 1.44 x 1.2, you have to ADD their logs together =0.15836 + 0.07918 =0.23754

1.44 x 1.2 =1.728

10^(0.23754) =1.728 - I dont think they expect you to calculate this step "BY HAND"!.

Apr 29, 2019
#2
+1

How did you get 2 = 0.07918?

Guest Apr 29, 2019
#3
+1

1.2 x 1.2 =1.44. Then:

1.2 x 1.2 =log(1.44)

1.2 x 1.2 =0.15836 . Remember what I said. When you multiply 2 numbers by each other, you must ADD their logs.

log(1.2) + log(1.2) =0.15836.

0.15836 divide it by 2 =0.07918 - This is log of 1.2, because:

log(1.2) =0.07918 + log(1.2) =0.07918 =log(1.44) =0.15836, or just:

.07918 + 0.07918 =0.15836 [You ADD the 2 logs of 1.2 together to get the log of 1.44]. Got it?

Apr 29, 2019