Question

How do I solve for X? 81^x=1/3

Answer 1

Solution 1:

81ˣ = 1/3

~Take log of both sides

log(81ˣ) = log(1/3)

x * (log(81)) = log(1/3)

$x = \frac{log(\frac{1}{3} )}{log(81)}$

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!