Solution 1:
81ˣ = 1/3
~Take log of both sides
log(81ˣ) = log(1/3)
x * (log(81)) = log(1/3)
[tex]x = \frac{log(\frac{1}{3} )}{log(81)}[/tex]
x = -0.25
Solution 2:
~Convert 81ˣ to a base of 3
81ˣ = (3⁴)ˣ
(3⁴)ˣ = 1/3
~Apply exponent rule of 1/aᵇ = a⁻ᵇ
1/3 = 3⁻¹
(3⁴)ˣ = 3⁻¹
~Apply exponent rule of (aᵇ)^c = a^bc
(3⁴)ˣ = 3^4x
3^4x = 3^-1
~Apply rule if a^f(x) = a^g(x), then f(x) = g(x)
4x = -1
~Divide 4 to both sides
4x/4 = -1/4
~Simplify
x = -0.25
Best of Luck!
