Question

If log ax2 – 5x + 8 = 2, then x =[​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of x = 2 , 3

Correct question :

$\displaystyle \sf \: \: log_{a} {a}^{ {x}^{2} - 5x + 8 } = 2 \: \: then \: \: x =$

Given

$\displaystyle \sf log_{a} {a}^{ {x}^{2} - 5x + 8 } = 2$

To find :

The value of x

Formula :

We are aware of the formula on logarithm that

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

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

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

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

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf log_{a} {a}^{ {x}^{2} - 5x + 8 } = 2$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf log_{a} {a}^{ {x}^{2} - 5x + 8 } = 2$

$\displaystyle \sf{ \implies }({x}^{2} - 5x + 8) log_{a} {a}^{ } = 2\: \: \: \bigg[ \: \because \: log( {a}^{n} ) = n log(a)\bigg]$

$\displaystyle \sf{ \implies }({x}^{2} - 5x + 8) \times 1 = 2\: \: \: \bigg[ \: \because \: log_{a} {a}^{ } = 1\bigg]$

$\displaystyle \sf{ \implies }({x}^{2} - 5x + 8) = 2$

$\displaystyle \sf{ \implies }{x}^{2} - 5x + 8 - 2 = 0$

$\displaystyle \sf{ \implies }{x}^{2} - 5x + 6 = 0$

$\displaystyle \sf{ \implies }{x}^{2} - (2 + 3)x + 6 = 0$

$\displaystyle \sf{ \implies }{x}^{2} - 2x - 3x + 6 = 0$

$\displaystyle \sf{ \implies }x(x - 2) - 3(x - 2) = 0$

$\displaystyle \sf{ \implies }(x - 2) (x - 3) = 0$

Now ,

x - 2 = 0 gives x = 2

x - 3 = 0 gives x = 3

Hence the required value of x = 2 , 3

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