Bonjour
a)
log(2x) = 3 avec x > 0 important !
10^(log(2x)) = 10^³
2x = 10^³
x = 10^³ / 2
x= 500 pour tout x > 0
b)
log(x/6)= 5 avec x > 0 important !
10^log(x/6) = 10^5
x/6 = 10^5
x = 6 * 10^5 = 600 000 avec x > 0
c)
log(5 * 3^x)= 10 avec x > 0 important !
log(5) + log(3^x)= 10
log(5) + x*log(3)= 10
x*log(3)= 10 - log(5)
x = ( 10 - log(5) ) / log(3)
d)
log(6^x / 4) = 9 avec x > 0 important !
log(6^x) - log(4) = 9
x*log(6) - log(4) = 9
x*log(6) = 9 + log(4)
x = (9 + log(4)) / log(6)
e)
log(x+5) = 4 avec x > 5 important !
10^log(x+5) = 10^4
x+5 = 10^4
x = 10^4 - 5
x= 9995
f)
log((x+3) / 5) = 5 avec (x+3) / 5 > 0 important !
10^log(x+3 / 5) = 10^5
(x+3) / 5 = 100000
(x+3) = 500000
x = 500000 - 3
x = 499997
g)
log(5x+9) = 6 avec 5x+9 > 0 important !
10^log(5x+9) = 10^6
5x + 9 = 10^6
5x = 10^6 - 9
x = (10^6 - 9)/5
h)
log((5^x+12)/ 6) = 1 avec (5^x+12)/ 6 > 0 important !
10^log((5^x+12)/ 6) = 10^1
(5^x+12)/ 6 = 10
(5^x+12) = 10 * 6
5^x+12 = 60
5^x = 60 - 12
5^x = 48
log(5^x) = log(48)
x*log(5) = log(48)
x = log(48) / log(5)
x = log₅(48) --> Log de base 5 si tu connais.
Bon courage
