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Ryan92560
@Ryan92560
December 2019
1
10
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Calcule o valor de X:
A-㏒ 3 81=X
B-㏒ 2√2 1/64=X
C-㏒ X 10.000=4
D-㏒ X 8/27=3
E-㏒ 8 (X-3= 1/3
F-㏒ 0,04 25=X
G-㏒ 27 √243=X
H-㏒ 100 0,01=X
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vandy091
Ryan, bom dia.
a)
log 3 (81) = x
Pela definição de logaritmo temos
3^x=81
3
^x=
3
^4
x=4
b)
log2√2 (1/64)= x
(2√2)^x=1/64
(2√2)^x=(1/2)^6
(2√2)^x=(2^-1)^6
(2√2)^x=2^-6
((2√2)^x)²=(2^-6)²
(4*2)^2x=4^-12
(2³)^2x=(2²)^-12
2
^6x=
2
^-24
6x=-24
x=-24/6
x=-4
c)
log x (10.000)=4
x^4=10.000
x^4=10^4
√(x^4)=√(10^4) (considere raiz de índice 4)
x=10
d)
log x ( 8/27) = 3
x³=8/27
x=∛(8/27)
x=2/3
e)
log8 (x-3)=1/3
8^1/3 = x-3
∛8 = x-3
2=x-3
x=5
f)
log0,4 (25) = x
log 4/100 (25) = x
log 1/25 (25) = x
(1/25)^x=25
((25)^-1)^x=25
25^-x=25
-x=1 (-1)
x=-1
g)
log27 (√243) = x
27^x=√(3*3*3*3*3)
(3³)^x=(3)^5/2
3^3x=3^5/2
3x=5/2
x=5/6
h)
log100 (0,01)=x
log10^2 (10^-2)=x
(10²)^x=(10^-2)
10^2x=10^-2
2x=-2
x=-1
Espero ter ajudado.
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Lista de comentários
a)
log 3 (81) = x
Pela definição de logaritmo temos
3^x=81
3^x=3^4
x=4
b)
log2√2 (1/64)= x
(2√2)^x=1/64
(2√2)^x=(1/2)^6
(2√2)^x=(2^-1)^6
(2√2)^x=2^-6
((2√2)^x)²=(2^-6)²
(4*2)^2x=4^-12
(2³)^2x=(2²)^-12
2^6x=2^-24
6x=-24
x=-24/6
x=-4
c)
log x (10.000)=4
x^4=10.000
x^4=10^4
√(x^4)=√(10^4) (considere raiz de índice 4)
x=10
d)
log x ( 8/27) = 3
x³=8/27
x=∛(8/27)
x=2/3
e)
log8 (x-3)=1/3
8^1/3 = x-3
∛8 = x-3
2=x-3
x=5
f)
log0,4 (25) = x
log 4/100 (25) = x
log 1/25 (25) = x
(1/25)^x=25
((25)^-1)^x=25
25^-x=25
-x=1 (-1)
x=-1
g)
log27 (√243) = x
27^x=√(3*3*3*3*3)
(3³)^x=(3)^5/2
3^3x=3^5/2
3x=5/2
x=5/6
h)
log100 (0,01)=x
log10^2 (10^-2)=x
(10²)^x=(10^-2)
10^2x=10^-2
2x=-2
x=-1
Espero ter ajudado.