United States l can you solve?? l Olympiad Math

[@val3val354]

Отлично! Очень доходчиво для школьников. Ты очень хороший преподаватель.

[@haiderlughmani]

Thank you ❣️

[@zawatsky]

2*7^a=140⇔7^a=70⇔7^(a-1)=10⇔a-1=log₇10=1/lg7⇔a=1+1/lg7.

[@stpat7614]

7^a + 7^a = 140
2 * 7^a = 140
(1/2) * 2 * 7^a = (1/2) * 140
1 * 7^a = 70
log(7^a) = log(70)
a * log(7) = log(70)
a * log(7) / log(7) = log(70) / log(7)
a * 1 = log(70) / log(7)
a = log_7(70)
a = log_7(2 * 5 * 7)
a = log_7(2) + log_7(5) + log_7(7)
a = log_7(2) + log_7(5) + 1
Verify:
7^a + 7^a
= 2 * 7^a
= 2 * 7^(log_7[2] + log_7[5] + 1)
= 2 * 7^(log_7[2]) * 7^(log_7[5]) * 7^1
= 2 * 2 * 5 * 7 = 140
= 140

[@ronaldnoll3247]

x=LOG(7) 70;
x= 2.1833

[@AlexanderSemashkevich]

x=log70/log7=(log7+log10)/log7=1+1/log7≈1+1/0.845≈2.1834.
Deviation is about 0.0001.
2×7^2.1834≈140.029.

[@zawatsky]

log what?🤭