Question

The value of x in log (9/63) = 1/2 is:
2/49
81/240
1/49
1/3​

Answer 1

Answer:

answer is 1/49

x^1/2=9/63

x=(9/63)^2

x=1/49

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ log_{x} \bigg( \frac{9}{63} \bigg) = \frac{1}{2} }$

TO DETERMINE

The value of x

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

EVALUATION

$\displaystyle \sf{ log_{x} \bigg( \frac{9}{63} \bigg) = \frac{1}{2} }$

$\displaystyle \sf{ \implies log_{x} \bigg( \frac{1}{7} \bigg) = \frac{1}{2} }$

$\displaystyle \sf{ \implies log_{x}(1) - log_{x}(7) = \frac{1}{2} }$

$\displaystyle \sf{ \implies 0 - log_{x}(7) = \frac{1}{2} }$

$\displaystyle \sf{ \implies log_{x}(7) = - \frac{1}{2} }$

$\displaystyle \sf{ \implies {x}^{ - \frac{1}{2} } = 7}$

$\displaystyle \sf{ \implies {x}^{ -1 } = 49}$

$\displaystyle \sf{ \implies \frac{1}{x} = 49}$

$\displaystyle \sf{ \implies x = \frac{1}{49} }$

FINAL ANSWER

$\displaystyle \sf{ x = \frac{1}{49} }$

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