Question

Log49 7 =
log 0,2 625=
log=√3 27=
log2 144 - log2 9 =
log3 54+log3 1,5=

z gory dziekuje .

Answer 1

Log49 7 =log₄₉ 7=½log₇ 7=½*1=½
log 0,2 625=log₅₋₁5⁴=-1log₅5⁴=-1*4log₅5=-4
log√3 27=log√₃3³=2*3log3₃=6
log₂144 - log₂9 =log₂(144/9)=log₂16=log₂2⁴=4log₂2=4
log₃54+log₃ 1,5=log₃(54*1,5)=log₃81=log₃3⁴=4log₃3=4

Answer 2

Log₄₉ 7 = x
(ten + np. tu 49⁺ zapisz jako x tu się tego nie da zapisać:)
49⁺ = 7
(7²)⁺ = 7¹
7²⁺ = 7¹
2x = 1 /:2
x = ½
log₄₉ 7 = ½

log₀,₂ 625 = x
0,2⁺ = 625
(2/10)⁺ = 5⁴
(1/5)⁺ = 5⁴
(5⁻¹)⁺ = 5⁴
5⁻⁺ = 5⁴
-x = 4 /*(-1)
x = - 4
log₀,₂ 625 = -4

log√₃ 27 = x
(√3)⁺ = 27
(3¹/²)⁺ = 3³
½x = 3 /*2
x = 6
log√₃27 = 6

Do poniższych stosujemy wzory:
loga b + loga c = loga (b*c)
loga b - loga c = loga (b/c)

log₂ 144 - log₂ 9 = log₂ (144:9) = log₂ 16 = x
2⁺ = 16
2⁺ = 2⁴
x = 4
log₂ 16 = 4

log₃ 4 + log₃ 1,5 = log₃ (54*1,5) = log₃ 81 = x
3⁺ = 81
3⁺ = 3⁴
x = 4
log₃ 81 = 4