Question

Find the value of x in 81^x=1/3?​

Answer 1

Answer:

x = - $\frac{1}{4}$

Step-by-step explanation:

Using the rules of exponents

$(a^m)^{n}$ = $a^{mn}$ , $a^{-m}$ = $\frac{1}{a^{m} }$

Given

$81^{x}$ = $\frac{1}{3}$ [ note that 81 = $3^{4}$ ] , then

$(3^4)^{x}$ = $3^{-1}$ , that is

$3^{4x}$ = $3^{-1}$

Since the bases on both sides are equal, both 3, then equate exponents

4x = - 1 ( divide both sides by 4 )

x = - $\frac{1}{4}$

Answer 2

Answer:

x = -1/4

Step-by-step explanation:

$81^{x}$ = 1/3

$3^{4}^{x}$ = $3^{-1}$

4x = -1

x = -1/4