determine the value of the following
(i)log 1 base 7
(ii)log root x base x
(iii)log 512 base 2
(iv)log 0.01 base 10
(v)log (8÷7) base 2÷3
(vi)2 power 2+log 3 base 2
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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.
Step-by-step explanation:
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