Question

Solve ; 4^2x = 1/32
solve plz its urgent ....

Answer 1

Question:

$\sf Solve :4^2^x = \dfrac{1}{32}$

Answer:

$\bigstar$ Given:

$\implies \sf 4^2^x = \dfrac{1}{32}$

$\bigstar$ To Find:

$\implies \sf x$

$\bigstar$ Solution:

From the above equation,

⇒ 4 can be written as $\sf 2^2$  

Since, $\sf 2^2$ = 2 * 2 = 4

$\sf \implies \dfrac{1}{32} can\;be\;written \;as \;(\dfrac{1}{2}) ^5$

$\sf Since,\; \dfrac{1}{32} = \dfrac{1}{2*2*2*2*2} =(\dfrac{1}{2})^5$

Therefore,

$\implies \sf {(2^2)^2^x} = \dfrac{1}{2} ^5$

$\implies \sf {(2)^4^x} = \dfrac{1}{2} ^5$

According to Property,

$\boxed{\sf Since,\;{(a^m)^n = a ^m^n}}$

$\implies \sf {2 ^4^x} = 2^-5$

According to property,

$\boxed{\sf {Since,\; \dfrac{1}{n}^x = n^-x}}\\\\\bullet \rm Only\; applicable\; for\; \dfrac{1}{n}^x\\\\\rm where,\\ \;n = 1,2,3.... \\ x = 1,2,3....$

As we can see here,

Bases are equal i.e, 2

Therefore powers can be equated.

Therefore,

$\sf 4x = -5$

Hence,

$\red \boxed{\boxed{x = \dfrac{-5}{4} }}$