Question

2 log power 5 base 10 - 8/27 log power 16base 10 + 3 log power 2 base 10 simplify​

Answer 1

Answer:

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Answer 2

Answer:

Let x denote the required logarithm.

Therefore, log2√3 1728 = x

or, (2√3)x = 1728 = 26 ∙ 33 = 26 ∙ (√3)6

or, (2√3)x = (2√3)6

Therefore, x = 6.

(ii) 0.000001 to the base 0.01.

Solution:

Let y be the required logarithm.

Therefore, log0.01 0.000001 = y

or, (0.01y = 0.000001 = (0.01)3

Therefore, y = 3.

2. Proof that, log2 log2 log2 16 = 1.

Solution:

L. H. S. = log2 log2 log2 24

= log2 log2 4 log2 2

= log2 log2 22 [since log2 2 = 1]

= log2 2 log2 2

= 1 ∙ 1

= 1. Proved.