Question

find x if 6^2x divided 6^-4 = 36

Answer 1

Answer:

x = -1

Step-by-step explanation:

We know that,

$\huge{ \mathfrak\color{violet}{{a}^{m} \div {a}^{n} = {a}^{m - n}} }$

$\: \: \: \: \sf{\large{ {6}^{2x} \div {6}^{ - 4} = 36 } }\\ \\ \sf\large\Rightarrow{6}^{2x - ( - 4)} = 36 \\ \\ \sf\large\Rightarrow \: \: \: \: \: {6}^{2x + 4} = {6}^{2} \\ \\ \sf\large\Rightarrow \: \: \: 2x + 4 = 2 \: \: \\ \\\sf \large\Rightarrow \: \: \: \: 2 x = 2 - 4 \\ \\ \sf\large\Rightarrow \: \: \: \: 2x = - 2 \: \: \: \: \\ \\ \sf\large\Rightarrow \: \: \: \: \: \: x = \frac{ - 2}{2} \: \: \: \\ \\ \sf\large \pink{ \: \: \: \therefore \: \color{lightgreen}{x = - 1}}$

$\huge{ \pink{N}\mathfrak \color{purple}{ot{ \pink e } }} : \color{black}{ - }$

$\large{ \mathfrak \color{orange}{ if \: \: \: {a}^{m} = {a}^{n} , \: \:then \: \: m = n}}$

Answer 2

Step-by-step explanation:

$\frac{6 {}^{2x} }{6 {}^{ - 4} } = 36$

$= > \frac{6 {}^{2x} }{6 {}^{ - 4} } = 6 {}^{2}$

$= > 6 {}^{2x + 4} = 6 {}^{2}$

base are same so we will compare the powers.

$= > 2x + 4 = 2$

$= > 2x = 2 - 4$

$2x = - 2$

$= > x = \frac{ - 2}{2}$

$= > x = - 1$