Question

If 5−4x × 5(x2+4) = 1, then find the value of ‘x’.​

Answer 1

Answer:

5-4x×5(x2+4)=1

5-4x×10x+20=1

5+20-4x×10x=1

25-40x=1

-40x=1-25

-40x=-24

x=-24/-40

x=0.6

Therefore, the value of x is 0.6

Answer 2

The value of x = 2

Given :

$\displaystyle \sf{ {5}^{ - 4x} \times {5}^{( {x}^{2} + 4) } = 1}$

To find :

The value of x

Formula :

We are aware of the formula on indices that

$\sf{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ {5}^{ - 4x} \times {5}^{( {x}^{2} + 4) } = 1}$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf{ {5}^{ - 4x} \times {5}^{( {x}^{2} + 4) } = 1}$

$\displaystyle \sf{ \implies {5}^{ (- 4x) +( {x}^{2} + 4) } = 1}\: \: \: \bigg[ \: \because \: {a}^{m} \times {a}^{n} = {a}^{m + n} \bigg]$

$\displaystyle \sf{ \implies {5}^{ ( {x}^{2} - 4x + 4) } = 1}$

$\displaystyle \sf{ \implies {5}^{ ( {x}^{2} - 4x + 4) } = {5}^{0} }$

$\displaystyle \sf{ \implies ( {x}^{2} - 4x + 4) = 0}$

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

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

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

Hence the required value of x = 2

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