Digits with logarithm

Algebra Level 2

Given that log ⁡ 3 = 0.477 \log 3 = 0.477 , how many digits are there if we expand 9 50 9^{50} ?


The answer is 48.

Ritchel Densing by Ritchel Densing , 40, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

log ⁡ 3 = 0.477 ⇒ log ⁡ 9 50 = log ⁡ 3 100 = 100 ⋅ log ⁡ 3 = 47.7 ⇒ \log 3 = 0.477 \Rightarrow \log 9^{50} = \log 3 ^{100} = 100 \cdot \log 3 = 47.7 \Rightarrow the number of digits of 9 50 9^{50} is 48 because 1 0 47 ( 48 d i g i t s ) < 9 50 = 1 0 47.7 < 1 0 48 ( 49 d i g i t s ) 10^{47} (48 digits) < 9^{50} = 10^{47.7} < 10^{48} (49 digits)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...