Question

Q9. If 6( 5x-5x-1)=120 ,then find the value of x

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Answer 1

Step-by-step explanation:

30x-30x-6=120

x-6=120

x= 120+6

x= 126

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Answer 2

Appropriate Question :-

If $\large\sf{6( {5}^{x} - {5}^{x - 1} ) = 120}$, then find the value of x.

Answer :-

Value of x = 2.

Solution :-

$\implies\sf{6( {5}^{x} - {5}^{x - 1} ) = 120}$

$\implies\sf{({5}^{x} - {5}^{x} \times {5}^{ - 1} ) = \dfrac{120}{6} }$

$\implies\sf{{5}^{x}(1 - {5}^{ - 1} ) = 20}$

$\implies\sf{{5}^{x}\bigg(1 - \dfrac{1}{5} \bigg ) = 20}$

$\implies\sf{{5}^{x}\bigg( \dfrac{5 - 1}{5} \bigg ) = 20}$

$\implies\sf{{5}^{x} \times \dfrac{4}{5} = 20}$

$\implies\sf{ {5}^{x} = \dfrac{ 20 \times 5}{4} }$

$\implies\sf{ {5}^{x} = 25}$

$\implies\sf{ {5}^{x} = {5}^{2} }$

$\implies\underline{\boxed{\tt\red{ x = 2}}}$

Therefore, Value of x = 2.