Question

If log52 - log5x = 4, what is the value of x?​

Answer 1

Step-by-step explanation:

log5x = 4 is the same as

54 = x

625 =x 

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ log_{5}(2) - log_{5}(x) = 4 }$

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

$\displaystyle \sf{ log_{5}(2) - log_{5}(x) = 4 }$

$\displaystyle \sf{ \implies log_{5} \bigg( \frac{2}{x} \bigg) = 4 }$

$\displaystyle \sf{ \implies \bigg( \frac{2}{x} \bigg) = {5}^{4} }$

$\displaystyle \sf{ \implies \bigg( \frac{2}{x} \bigg) = 625}$

$\displaystyle \sf{ \implies x = \frac{2}{625} }$

FINAL ANSWER

$\displaystyle \sf{ x = \frac{2}{625} }$

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