Question

1. Exprese cada forma exponencial en forma logarítmica
a) 10^4 = 10000
b) 8 2/3=4 (fraccion /)
c) e^2= 7,3891
d) 3^−4 =1/81
2. Exprese cada forma logarítmica en forma exponencial
a) ln ^−2 = −2
b) log12 144 = 2
c) log 0,001 = −3
d) log √1000 =3/2
3. Desarrolle la demostración de la siguiente propiedad de los logaritmos
log (1/) = − log N

Answer 1

Respuesta:

Explicación:

a) 10^4 = 10000

log 10⁴ = log 10000

4 log 10 = log 10⁴

4(1) = 4 log 10

4 = 4

b) 8^2/3=4

log (8)^2/3 = log 4

(2 / 3) log 8 = log 4

log 8 = (3 log 4) / 2

log 2*4 = (3 log 4) / 2

log 2 + log 4 = (3 log 4) / 2

log 2 = (3 log 4) / 2 - log 4

log 2 = (3 log 4 - 2 log 4) / 2

log 2 = log 4 / 2

2 log 2 = log 4

log 2² = log 4

log 4 = log 4

c) e^2= 7,3891

ln e² = ln 7,3891

e² = 7,3891

2 ln e = ln e²

2 ln e = 2 ln e

2(1) = 2(1)

2 = 2

d) 3^−4 =1/81

3⁻⁴ = 1 / 81

log 3⁻⁴ = log (1/81)

-4 log 3 = log (1 / 3⁴)

-4 log 3 = log (3⁻⁴)

-4 log 3 = -4 log 3

-4 = -4

a) ln ^−2 = −2

ln e⁻² = −2

-2 ln e = -2

-2 = -2

b) log12 144 = 2

log₁₂ 144 = 2

log₁₂ 12² = 2

2 log₁₂ 12 = 2

2(1) = 2

2 = 2

c) log 0,001 = −3

log 0,001 = −3

log (1/1000) = -3

log (1 / 10³) = -3

log (10⁻³) = -3

-3 log 10 = -3

-3(1) = -3

-3 = -3

d) log √1000 =3/2

log √1000 = 3/2

log √10³ = 3/2

log (10³)^1/2 = 3/2

log (10^3/2) = 3/2

3/2 log 10 = 3/2

3*(1)/2 = 3/2

3/2 = 3/2

Desarrolle la demostración de la siguiente propiedad de los logaritmos

log (1/N) = − log N

log (N⁻¹ ) = - log N

(-1) log N = - log N

- log N = - log N