Respostas
1) s=3.log0.001+2.log₁/₃9-log₅625
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log0.001 subentende que a base e 10
log₁₀0.001=n s3ja 0.001 =10-³
log 10ⁿ=10-³
n=-3
log₁/₃9=n
log (1/3)ⁿ=9
log(3)-ⁿ=3²
-n=2 =n=-2
log₅625=n
log 5ⁿ=625
log 5ⁿ=5⁴
n=4
substituindo os valores encontrados nesta expressao s=3*log0.001+2*log₁/₃9-log₅625 ficara
s=3*(-3)+2*(-2)-4
s=-9+2*(-2)-4
s=-9-4-4= -17
2)
a) log₃81=n
3ⁿ=3⁴
n=4
b)log₅125=n
5ⁿ=5⁵
n=5
c) log 10000=n
log10ⁿ=10⁴
n=4
d)log₁/₂32=n
log(1/2)ⁿ=2⁵
(2)-ⁿ=2⁵
n=-5
log0.01
log 10ⁿ=10-²
n=-2
log₂0.5
log2ⁿ=1/2
n=-1
E) log₄√(128)=n
4ⁿ=128¹/²
2²ⁿ=2⁷/²
2n=7/2
n=7/4
f)log₀,₅64=n
1/2ⁿ=2⁶
n=-6
3) log₂1024+log₁/₅625
log 2ⁿ=1024
n=10
log (1/5)ⁿ=625
n=-4
s=10-4=6
4)
a)log₃ 81
3ⁿ=81
n=4
b)log₂₅0.2
25ⁿ=(1/5)
2n=-1
n=-1/2
c)Log 16ⁿ=32
log2⁴ⁿ=2⁵
n=5/4
d) log5ⁿ=64/1000000
log5ⁿ=1/15625
logⁿ=1/5⁶
n=-6
e)log2ⁿ=1/4
log2ⁿ=1/2²
n=-2
F) log₄√(128)=n
log 4ⁿ=128¹´²
2²ⁿ=2⁷´²
2n=7/2
4n=7
n=7/4
g)log₅√(125)=n
5ⁿ=125¹´²
5ⁿ=5³´²
n=3/2
h) log₁/₈√(128)=n
1/8ⁿ=128¹´²
2-³ⁿ=2⁷´²
-3n=7/2
n=-7/6
i) log₄√(512)=n
4ⁿ=512¹´²
2²ⁿ=2⁹´²
2n=9/2
n=9/4