Question

Logarytmy ;))
13 przykładów, są one w załączniku...

Dzięki ;P

Answer 1

A)
log₂5 * log₅32 = log₂5 *log₅2⁵ = log₂5*5*log₅2 =
= 5*log₂5 *[1/log₂5] = 5
b)
log₈ 81 * log₉ 8 = log₈ 9² *log₉ 8 = 2*log₈ 9* [1/log₈ 9] = 2
c)
log₄ 5 * log₅ 256 = log₄ 5 * log₅ 4⁴ = log₄ 5 *4* log₅ 4 =
= 4* log₄ 5 *[1/log₄ 5] = 4
d)
2 log₄ 8 - 7⁰ = log₄ 8² - 1 = log₄ 64 - 1 = 3 - 1 = 2
e)
log₅ 750 - log₅ 6 = log₅ [750 : 6] = log₅ 125 = 3 , bo 5³ = 125
f)
log 2 + log 500 = log [2*500] = log 1000 = 3, bo 10³ = 1000
h)
log 1 = [log₂ 4]³ + log₂ 4³ = 0 + 2³ + 3* log₂ 4 =
= 0 + 8 + 3*2 = 8 + 6 = 14
i)
-[ log₈ 64]² - 2*log₈ 64² = - 2*log₈ 64 -2*2* log₈ 64 =
= -2*2 - 4*2 = -4 - 8 = -12, bo log₈ 64 = 2 gdyż 8² = 64