Question

log2 10 - Log2 5 + log2 8

Answer 1

log 2 10 - log 2 5 + log 2 8 = log 2 ( 10 * 8 / 5 ) = log 2 ( 2 * 8 ) = log 2 ( 16 ) = log 2 ( 2 ^ 4 ) = 4

ответ: 4

Answer 2

Сумма и разность логарифмов по одному основанию.

logₐb - logₐc=logₐ(b/c)

logₐb + logₐc=logₐ(b*c);   a; b; c >0; a≠1

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log₂10 - log₂5=log₂(10/5)=log₂2

log₂2 + log₂8=log₂(2*8)=log₂16=log₂2⁴=4.

ИЛИ

log₂10 - log₂5 + log₂8=log₂(10/5 * 8)=log₂16=log₂2⁴=4.

ИЛИ

log₂10 - log₂5=log₂(10/5)=log₂2¹=1

1 + log₂8=1+log₂2³=1+3=4.

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Answer 3

log2 10 = log2(2*5) = log2(2) + log2(5) = 1 + log2 5

log2 8 = log2(2^3) = 3log2 2 = 3

Therefore,

log2 10 - log2 5 + log2 8 = (1 + log2 5) - log2 5 + 3 = 4.