If-7-243-a-bc-Find-b-c-

Question Number 209719 by hardmath last updated on 19/Jul/24

If :

7^{243} = \overset{―}{a \dots bc}

Find :

b \cdot c = ?

Answered by MM42 last updated on 19/Jul/24

7^{4} \overset{100}{\equiv} 1 \Rightarrow 7^{240} \overset{100}{\equiv} 1 \Rightarrow 7^{243} \overset{100}{\equiv} 7^{3} \overset{100}{\equiv} 43

\Rightarrow b c = 12 ✓

Commented by hardmath last updated on 19/Jul/24

thank you dear professor, but a = ?

Commented by MM42 last updated on 19/Jul/24

I d o n t k n o w

Commented by Frix last updated on 22/Jul/24

\log_{10} 7^{243} = {243 \log}_{10} 7 \approx 243 \times . 845098 \approx

\approx 205.359

7^{243} \approx 10^{205} \times 10^{. 359}

10^{. 359} \approx 2.29

7^{243} \approx 2.29 \times 10^{205}

a = 2

Facebook Tweet Pin