logx^2{base3}=-8
show that x=1/27
not that dificult
logx^2=-8
x^2=3^-8
x^2=3^(-2)^3
power 2 cancel out we have
x=3^-3
x=1/3^3
x=1/27
or
log3 x^2 = -8
2 log3 x = -8
3 x = -4
x = 3^-4
x = 1/81 not 1/27
check with calculator
if x = 1/27
3 (1/27)^2
= 23 (1/27)
= 2(-3)
= -6
≠ -8
1/81 does check out.
oh yeah i did not see that thanks.....
To solve the equation log₃(x²) = -8, we can rewrite it using logarithmic properties.
First, recall the logarithmic property that states logₐ(b) = c if and only if aᶜ = b.
Using this property, we can rewrite the equation as 3⁻⁸ = x².
Simplifying further, we have 1/3⁸ = x².
Now, taking the square root of both sides to isolate x, we get √(1/3⁸) = x.
Simplifying the square root, we have 1/3⁴ = x.
Finally, simplifying 3⁴, we get 1/81 = x.
Therefore, x = 1/81, which means x = 1/27 in its simplified form.