Question

Ques. Which of the following is log8(x) equivalent to?

Op 1: log2(x/3)
Op 2: log2(3x)
Op 3: (log2x)/ 3
Op 4: None of these

Answer 1

Answer:

Op 3

Step-by-step explanation:

log8(x) = log2³(x)

as 2³ is the base, the power of the base is divided with the log value

answer is,

1/3•log2x

Answer 2

Answer:

Required value is $\frac{1}{3}log_{2}{x}$

So, option 3 is the right answer.

Step-by-step explanation:

Given,

$log_{8}(x)$

Here we want to find value of this.

Let,

$y = log_{8}(x)$

$y = log_{{2}^{3}}(x)$

$y = \frac{logx}{3 log_(2)} \\ =\frac{1}{3}log_{2}{x}$

Here applied formula,

$log( {x}^{a} ) = a log(x)$

Some important Logarithm formulas,

$log_{x}(1) = 0 \\ log_{x}(0) = 1 \\ log_{x}(y) = \frac{ log(x) }{ log(y) } \\ log( {x}^{y} ) = y log(x) \\ log(x) + log(y) = log(xy) \\ log(x) - log(y) = log( \frac{x}{y} ) \\ log_{x}(x) = 1$

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