3. @ Angel Prieto Benito Matemáticas Aplicadas CS I 3
• Hallar el valor del logaritmo en:
• log3 27 = x ↔ 3x
= 27 3x
= 33
x = 3
• log5 0,2 = x ↔ 5x
= 0,2 5x
= 1/5 5x
= 5– 1
x = – 1
• log10 1 = x ↔ 10 x
= 1 10 x
= 10 0
x = 0
• log27 3 = x ↔ 27 x
= 3 (33
) x
= 3 3 3.x
= 3
• 3 3.x
= 3 1
3.x = 1 x = 1/3
• Log1/2 1/4 = x ↔ (1/2) x
= 1 / 4 1 / 2 x
= 1 / 2 2
x = 2
EJERCICIOS (II)
4. @ Angel Prieto Benito Matemáticas Aplicadas CS I 4
• Hallar el número N al que se aplica el logaritmo en:
• log3 N = 3 ↔ 33
= N N = 27
• log5 N = - 2 ↔ 5-2
= N N = 1 / 25 = 0,04
• log36 N = 1/2 ↔ 361/2
= N N = (62
)1/2
= 6
• log2 N = - 4 ↔ 2 - 4
= N N = 1/16
• log1/2 N = 3 ↔ (1/2)3
= N N = 1 / 23
= 1 / 8
• ln N = 3 ↔ e3
= N N = e3
= 20,09
EJERCICIOS (y III)